AI-Driven Risk Management for Nordic Power Futures and GoO Portfolios

AI-Driven Risk Management for Nordic Power Futures and GoO Portfolios


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The Nordic power market is one of the world’s most liquid and sophisticated electricity markets, trading over 500 TWh annually across Norway, Sweden, Finland, and Denmark. Power producers, industrial consumers, and financial players manage portfolios worth billions of euros, exposed to extreme price volatility driven by weather patterns, hydroelectric reservoir levels, wind generation variability, and cross-border transmission constraints. A single winter storm can swing prices from €50/MWh to €500/MWh within hours. A mild autumn can crash prices to near-zero as hydroelectric reservoirs overflow. Managing risk in this environment is not optional—it’s existential.

Traditional risk management approaches—Value-at-Risk (VaR) calculated from historical volatility, linear correlation assumptions, Gaussian distributions—systematically underestimate tail risks in power markets. These methods were designed for liquid financial assets with relatively stable correlations and continuous price distributions. Nordic power markets violate all these assumptions: prices exhibit fat tails, regime switching, non-linear weather dependencies, and structural breaks when transmission lines reach capacity. The result: risk models that work fine 95% of the time catastrophically fail during the 5% of periods that actually matter—the extreme events that bankrupt companies.

In 2021, during the European energy crisis, dozens of Nordic power trading firms and retailers went bankrupt because their risk models failed to capture the compound effects of low wind generation, high natural gas prices, and reduced nuclear capacity. Companies that survived weren’t just lucky—many had adopted machine learning-based risk models that could capture non-linear dependencies traditional methods missed. This article examines how artificial intelligence and machine learning transform risk management for Nordic power futures and Guarantees of Origin (GoO) portfolios, providing mathematical rigor, Python implementations, and real-world case studies.

The Nordic Power Market Landscape

Before discussing AI applications, we must understand what makes Nordic power markets unique and why they require specialized risk management.

Market Structure

The Nordic power market operates through Nord Pool, Europe’s leading power exchange. Trading occurs in multiple timeframes:

Day-Ahead Market (Elspot): Participants submit bids and offers for each hour of the following day. Nord Pool clears the market at noon, determining a system price (reference price for the entire Nordic region) and area prices (local prices reflecting transmission constraints). This is where most hedging occurs.

Intraday Market (Elbas): Continuous trading up to 1 hour before delivery, allowing participants to adjust positions as forecasts improve. Prices can deviate significantly from day-ahead as real-time conditions (wind forecasts, plant outages) evolve.

Financial Derivatives: Futures, forwards, options, and swaps traded both on exchange (NASDAQ Commodities) and OTC (over-the-counter). Contracts range from weekly to annual, with the most liquid being quarterly and yearly forwards.

Price Areas: The Nordic region is divided into bidding zones (NO1-NO5 for Norway, SE1-SE4 for Sweden, DK1-DK2 for Denmark, FI). Transmission bottlenecks between areas create basis risk—the spread between local area price and system price. A hydropower producer in NO4 (Southern Norway) might hedge using system price futures but face losses if NO4 trades at a premium due to transmission constraints.

Supply Characteristics

Hydropower dominance: Norway and Sweden derive 60-90% of electricity from hydroelectric generation. This creates unique risk dynamics: reservoir levels (measured in TWh of stored energy) become the primary price driver. High reservoir levels → low prices (abundant supply). Low reservoirs + cold winter → price spikes.

Wind generation volatility: Denmark and parts of Sweden rely heavily on wind (40-50% penetration). Wind is near-zero marginal cost but highly unpredictable. Forecast errors of 20-40% are common 24 hours ahead, causing day-ahead market prices to frequently miss actual conditions.

Interconnections: The Nordics are heavily interconnected with continental Europe, the UK, and the Baltics via HVDC cables. These cables have limited capacity (typically 1-4 GW). When transmission reaches capacity, Nordic prices can decouple dramatically from European prices—a key source of model risk.

Demand Patterns

Temperature sensitivity: Nordic electricity demand is highly temperature-dependent due to electric heating. A 1°C temperature drop in winter increases demand by approximately 1 GW. Winter demand can be 50% higher than summer.

Industrial baseload: Large industrial consumers (pulp/paper mills, aluminum smelters, data centers) provide baseload demand that’s relatively predictable but price-sensitive—smelters shut down when prices exceed production margins.

Guarantees of Origin (GoO): The Green Certificate Market

In parallel to physical power trading, the Nordic market has a sophisticated system for tracking renewable energy attributes through Guarantees of Origin certificates. Understanding GoO is critical for modern risk management because many portfolios combine physical power positions with environmental certificates.

What Are GoO Certificates?

A Guarantee of Origin is a electronic certificate proving that 1 MWh of electricity was generated from renewable sources (hydro, wind, solar, biomass). When a renewable plant generates power, it receives both:

  1. Physical electricity sold in the power market
  2. GoO certificate sold separately in the environmental market

This unbundling allows consumers anywhere in Europe to claim “green energy” by purchasing GoO certificates, even if they physically consume conventional power. A data center in Germany can buy cheap coal power locally while purchasing Nordic hydro GoO certificates to claim 100% renewable consumption.

GoO Market Dynamics

Supply: Heavily dominated by Nordic hydropower (stable, predictable) and wind (variable). Norway alone produces 130-150 TWh of hydro GoO annually.

Demand: Corporate renewable energy buyers (Google, Amazon, Microsoft, industrial companies), utilities fulfilling renewable obligations, consumers wanting green power.

Price formation: GoO prices are much more stable than power prices (typically €0.50-€2.00/MWh vs €20-€100/MWh for power) but exhibit their own dynamics:

  • Oversupply risk: When renewable generation exceeds demand for certificates, prices collapse (saw €0.10/MWh in 2020)
  • Technology premiums: Wind and solar GoOs trade at premiums to hydro due to “additionality” perceptions
  • Vintage effects: Newer certificates sometimes command premiums

Portfolio Correlation: Power + GoO

Many market participants hold combined portfolios:

  • Renewable generators: Sell both power and GoO certificates
  • Power retailers: Buy power, sometimes bundle with GoO for “green tariffs”
  • Industrial hedgers: May buy power and GoO separately to minimize cost while meeting sustainability targets

The correlation between power prices and GoO prices is complex and non-linear:

  • High power prices: Often correlate with low wind (high demand or low wind generation), reducing wind GoO supply, potentially raising GoO prices
  • Negative power prices: Can occur with excessive wind generation, but this produces abundant GoO supply, depressing GoO prices
  • Structural breaks: Policy changes (EU renewable targets, carbon pricing) create regime shifts in GoO demand

Traditional correlation matrices fail to capture these dynamics. AI models can learn time-varying, non-linear relationships.

Traditional Risk Management: Why It Fails

Before exploring AI solutions, let’s understand why conventional approaches systematically underestimate risk in Nordic power markets.

Value-at-Risk (VaR) with Historical Simulation

The standard industry approach:

  1. Collect historical price returns (e.g., 2 years of daily data)
  2. Calculate portfolio return for each historical scenario
  3. VaR(95%) = 5th percentile of historical portfolio returns
$$ \text{VaR}\_{95\%} = -\text{quantile}(R\_{\text{portfolio}}, 0.05) $$

where $R\_{\text{portfolio}}$ is the distribution of historical portfolio returns.

Why it fails for Nordic power:

Structural breaks: The energy transition is transforming the Nordic system. Wind capacity has tripled in the last decade. Nuclear plants have closed. Interconnector capacity has doubled. Historical data from 2015-2020 fundamentally doesn’t represent the 2024 market structure. Models trained on old data underestimate the impact of high wind penetration or new transmission lines.

Regime changes: Power markets exhibit distinct regimes—“normal” periods with prices in €30-€60/MWh range, and “stress” periods with €100-€500/MWh spikes. Historical VaR will underestimate risk if the historical window contains few stress events. A model estimated from 2018-2020 data (mild weather, ample supply) would catastrophically underpredict 2021-2022 risks (energy crisis, price spikes to €300+).

Non-Gaussian distributions: Power prices exhibit fat tails and negative skewness. Historical simulation captures this, but calculating VaR at extreme percentiles (99%, 99.9%) requires decades of data—which don’t exist in stationary form.

Parametric VaR with Correlation Matrices

Alternative approach: assume returns are multivariate normal, estimate covariance matrix, calculate VaR analytically.

$$ \text{VaR} = Z\_\alpha \sqrt{w^T \Sigma w} $$

where $w$ is the portfolio weight vector, $\Sigma$ is the covariance matrix, $Z\_\alpha$ is the normal quantile.

Why it fails:

Gaussian assumption: Power prices are decidedly non-normal. Assuming normality underestimates tail risk by 50-200%. A “4-sigma event” under Gaussian assumptions might actually be a 2-sigma event in the true distribution.

Linear correlations: Correlation matrices assume linear relationships. In power markets, correlations are state-dependent:

  • During normal conditions: NO1 (Eastern Norway) and NO5 (Western Norway) prices have 0.7 correlation
  • During transmission congestion: correlation drops to 0.3 or even negative (south imports expensive power while north has surplus)

Standard correlation matrices cannot capture “correlation breaks down exactly when you need it”—a failure mode that caused massive losses in 2021.

Example: The 2021 Nordic Energy Crisis

In Q4 2021, Nordic power prices spiked to record levels:

  • System price averaged €120/MWh (vs €30/MWh in Q4 2020)
  • Southern Norway (NO2) reached €200+/MWh for weeks
  • Many retailers and small producers went bankrupt

What traditional models predicted:

  • Historical VaR(99%): €80/MWh
  • Parametric VaR(99%): €90/MWh
  • Both models suggested hedging to €90/MWh would provide 99% confidence of avoiding losses

What actually happened:

  • Prices exceeded €150/MWh for extended periods
  • The compound effect of low wind, high gas prices (European market coupling), and low reservoir levels created a regime that hadn’t occurred in historical data
  • Linear correlation models failed to capture how multiple risk factors reinforced each other

Companies using machine learning models that could extrapolate beyond historical scenarios and capture non-linear dependencies fared significantly better.

AI and Machine Learning for Power Risk: The Paradigm Shift

Machine learning doesn’t just improve risk estimation—it fundamentally changes how we think about risk in power markets. Traditional methods ask: “What happened historically?” ML asks: “What patterns govern price formation, and how might those patterns evolve?”

Why ML Works for Power Markets

Non-linear relationships: Neural networks can learn that the relationship between temperature and price is exponential below 0°C (heating demand explodes), piecewise linear from 0-15°C, and flat above 15°C. Traditional models use linear temperature coefficients.

Feature engineering from physics: Power prices are ultimately determined by physics—thermodynamics (power plant efficiency curves), hydrology (rainfall patterns), meteorology (wind forecasts). ML models can incorporate weather forecasts, reservoir levels, plant availability as features, learning complex interactions.

Regime detection: Hidden Markov Models (HMMs) or clustering algorithms can identify latent market regimes (normal, tight supply, transmission congestion, price spike) and apply regime-specific risk models.

Tail risk extrapolation: Generative models (GANs, VAEs) can simulate scenarios beyond historical experience by learning the underlying data generation process.

Time-varying correlations: LSTM networks or Transformer models can learn how correlations evolve based on market conditions, weather patterns, and time of year.

Feature Engineering: The Foundation of ML Risk Models

The quality of ML risk models depends critically on feature engineering—transforming raw data (prices, weather, reservoir levels) into informative inputs that capture the physics and economics of power markets.

Temporal Features

Calendar effects:

  • Hour of day (demand patterns)
  • Day of week (weekday vs weekend consumption)
  • Month (seasonal patterns)
  • Holiday indicators (reduced industrial demand)
import pandas as pd
import numpy as np

def create_temporal_features(df):
    """
    Create temporal features from datetime index.

    Args:
        df: DataFrame with DatetimeIndex

    Returns:
        DataFrame with additional temporal features
    """
    df = df.copy()

    # Basic calendar features
    df['hour'] = df.index.hour
    df['day_of_week'] = df.index.dayofweek
    df['month'] = df.index.month
    df['quarter'] = df.index.quarter

    # Cyclical encoding (important for avoiding discontinuity at boundaries)
    # Hour: 0-23 → sin/cos representation
    df['hour_sin'] = np.sin(2 * np.pi * df['hour'] / 24)
    df['hour_cos'] = np.cos(2 * np.pi * df['hour'] / 24)

    # Day of week: 0-6
    df['dow_sin'] = np.sin(2 * np.pi * df['day_of_week'] / 7)
    df['dow_cos'] = np.cos(2 * np.pi * df['day_of_week'] / 7)

    # Month: 1-12
    df['month_sin'] = np.sin(2 * np.pi * (df['month'] - 1) / 12)
    df['month_cos'] = np.cos(2 * np.pi * (df['month'] - 1) / 12)

    # Nordic-specific: Heating/cooling season
    # Northern latitudes have strong seasonal demand
    df['is_winter'] = df['month'].isin([11, 12, 1, 2, 3]).astype(int)
    df['is_summer'] = df['month'].isin([6, 7, 8]).astype(int)

    # Public holidays (reduces demand)
    # Simplified - in production use holiday package
    df['is_holiday'] = 0

    return df

Why cyclical encoding? Hour 23 and hour 0 are adjacent in time but numerically distant (23 vs 0). Cyclical encoding using sine/cosine preserves temporal proximity, improving model learning.

Meteorological Features

Weather is the primary driver of both supply (wind, hydro inflows, solar) and demand (temperature, heating/cooling).

Temperature: Not just current temperature, but:

  • Heating Degree Days (HDD): $\max(18°C - T, 0)$ summed over days—captures cumulative cold
  • Cooling Degree Days (CDD): $\max(T - 22°C, 0)$
  • Temperature deviation from seasonal normal: Absolute temperature matters less than deviation from expected

Wind:

  • Forecasted wind generation: MW capacity × forecasted capacity factor
  • Forecast error: Historical wind forecast errors predict system stress
  • Spatial distribution: Wind in DK1 vs SE3 matters due to transmission constraints

Precipitation and snowmelt:

  • Cumulative rainfall: Predicts hydro inflows with 1-4 week lag
  • Snowpack: Spring snowmelt is major hydro inflow source
  • Evaporation: Temperature + humidity affects reservoir evaporation
def create_weather_features(df, temperature, wind_forecast, precipitation):
    """
    Create weather-derived features for power price modeling.

    Args:
        df: Base DataFrame with DatetimeIndex
        temperature: Series of temperature (°C)
        wind_forecast: Series of forecasted wind generation (MW)
        precipitation: Series of precipitation (mm/day)

    Returns:
        DataFrame with weather features
    """
    df = df.copy()

    # Temperature features
    df['temperature'] = temperature

    # Heating Degree Days (HDD) - base 18°C
    df['hdd'] = np.maximum(18 - temperature, 0)

    # Cooling Degree Days (CDD) - base 22°C
    df['cdd'] = np.maximum(temperature - 22, 0)

    # Temperature squared (capture non-linear effects)
    df['temp_squared'] = temperature ** 2

    # Temperature below freezing (triggers heating demand surge)
    df['temp_below_zero'] = (temperature < 0).astype(int)

    # Seasonal temperature deviation
    # Calculate rolling seasonal mean (365-day window)
    seasonal_mean = temperature.rolling(window=365, center=True).mean()
    df['temp_deviation'] = temperature - seasonal_mean

    # Wind features
    df['wind_forecast'] = wind_forecast

    # Wind capacity factor (0-1)
    installed_capacity = 10000  # MW - example value
    df['wind_capacity_factor'] = wind_forecast / installed_capacity

    # Wind forecast uncertainty (use ensemble spread if available)
    # Placeholder: use historical volatility as proxy
    df['wind_volatility'] = wind_forecast.rolling(window=168).std()  # 1 week

    # Precipitation features
    df['precipitation'] = precipitation

    # Cumulative precipitation (predicts hydro inflows)
    # 30-day rolling sum
    df['precip_30d'] = precipitation.rolling(window=30).sum()

    # 90-day rolling sum (seasonal reservoir filling)
    df['precip_90d'] = precipitation.rolling(window=90).sum()

    # Precipitation deviation from seasonal normal
    seasonal_precip = precipitation.rolling(window=365, center=True).mean()
    df['precip_deviation'] = precipitation - seasonal_precip

    return df

Fundamental Supply Features

Reservoir levels: The single most important feature for Nordic prices.

$$ \text{Reservoir Filling} = \frac{\text{Current Storage (TWh)}}{\text{Maximum Capacity (TWh)}} $$
  • High filling (>90%) → Prices drop (must generate to prevent overflow)
  • Low filling (<50%) → Prices rise (scarcity)
  • Critical levels (<30%) in winter → Price spikes risk

Generation capacity available:

  • Planned outages: Nuclear, thermal plants schedule maintenance
  • Forced outages: Unplanned failures (data from Nord Pool’s REMIT reporting)
  • Must-run constraints: Some plants must operate for grid stability

Fuel prices:

  • Natural gas (TTF, Dutch hub): Marginal price setter during high demand
  • Coal (European benchmarks): Less relevant now but historical importance
  • Carbon prices (EU ETS): Affects thermal generation costs
def create_fundamental_features(df, reservoir_level, gas_price, carbon_price, nuclear_capacity):
    """
    Create features from power market fundamentals.

    Args:
        df: Base DataFrame
        reservoir_level: TWh of stored hydro energy
        gas_price: EUR/MWh natural gas price
        carbon_price: EUR/ton CO2
        nuclear_capacity: MW available nuclear capacity

    Returns:
        DataFrame with fundamental features
    """
    df = df.copy()

    # Reservoir levels
    max_capacity = 120  # TWh for Nordic region
    df['reservoir_twh'] = reservoir_level
    df['reservoir_filling'] = reservoir_level / max_capacity

    # Reservoir filling relative to historical average for this time of year
    seasonal_avg = reservoir_level.groupby([df.index.month, df.index.day]).transform('mean')
    df['reservoir_deviation'] = reservoir_level - seasonal_avg

    # Low reservoir indicator (critical level)
    df['reservoir_critical'] = (df['reservoir_filling'] < 0.3).astype(int)

    # Rate of reservoir change (weekly change)
    df['reservoir_change_weekly'] = reservoir_level - reservoir_level.shift(168)  # 1 week

    # Fuel prices
    df['gas_price'] = gas_price
    df['carbon_price'] = carbon_price

    # Thermal generation cost (gas + carbon)
    # Simplified: Gas plant efficiency ~50%, carbon intensity ~0.4 ton/MWh
    thermal_cost = gas_price / 0.5 + carbon_price * 0.4
    df['thermal_generation_cost'] = thermal_cost

    # Nuclear availability
    df['nuclear_capacity'] = nuclear_capacity
    df['nuclear_capacity_pct'] = nuclear_capacity / 10000  # % of installed capacity

    return df

Interconnection and Transmission Features

Flow levels: Actual power flow on major interconnections (NO-SE, NO-DK, SE-DK, Nordic-Continental Europe)

Utilization: $\text{Flow} / \text{Capacity}$—when approaching 100%, transmission constraints activate

Price spreads: Spread between area prices indicates congestion

def create_transmission_features(df, no_se_flow, no_se_capacity, no2_price, no5_price):
    """
    Create transmission/interconnection features.

    Args:
        df: Base DataFrame
        no_se_flow: MW flow from Norway to Sweden (positive = export)
        no_se_capacity: MW maximum capacity
        no2_price: Price in NO2 (Southern Norway)
        no5_price: Price in NO5 (Western Norway)

    Returns:
        DataFrame with transmission features
    """
    df = df.copy()

    # Interconnector utilization
    df['no_se_flow'] = no_se_flow
    df['no_se_utilization'] = np.abs(no_se_flow) / no_se_capacity

    # Congestion indicator (>90% utilization)
    df['no_se_congested'] = (df['no_se_utilization'] > 0.9).astype(int)

    # Price spreads (basis risk)
    df['no2_price'] = no2_price
    df['no5_price'] = no5_price
    df['no2_no5_spread'] = no2_price - no5_price

    # Spread volatility (indicates transmission risk)
    df['spread_volatility'] = df['no2_no5_spread'].rolling(window=168).std()

    return df

Machine Learning Models for Price Forecasting and Risk Simulation

With features engineered, we can build ML models for two core risk management tasks: (1) price forecasting, and (2) scenario generation for risk metrics (VaR, CVaR).

Gradient Boosting for Deterministic Price Forecasting

Gradient boosted trees (XGBoost, LightGBM, CatBoost) excel at capturing non-linear relationships and feature interactions in tabular data. They’re interpretable (feature importance), fast, and robust to outliers.

Architecture: Ensemble of decision trees, each tree correcting errors of previous trees.

Use case: Day-ahead price forecasting, or forecasting price distribution parameters (mean, volatility).

import pandas as pd
import numpy as np
from lightgbm import LGBMRegressor
from sklearn.model_selection import TimeSeriesSplit
from sklearn.metrics import mean_absolute_error, mean_squared_error

def train_price_forecast_model(df, target_col='price', n_lags=24):
    """
    Train gradient boosting model for power price forecasting.

    Args:
        df: DataFrame with features and target
        target_col: Name of target column (price)
        n_lags: Number of lagged price features to include

    Returns:
        Trained model and feature names
    """
    # Create lagged price features
    for lag in range(1, n_lags + 1):
        df[f'price_lag_{lag}'] = df[target_col].shift(lag)

    # Create rolling statistics
    df['price_rolling_mean_24h'] = df[target_col].shift(1).rolling(window=24).mean()
    df['price_rolling_std_24h'] = df[target_col].shift(1).rolling(window=24).std()
    df['price_rolling_mean_168h'] = df[target_col].shift(1).rolling(window=168).mean()

    # Drop NaN rows from lagging
    df = df.dropna()

    # Split features and target
    feature_cols = [col for col in df.columns if col != target_col and col != 'price']
    X = df[feature_cols]
    y = df[target_col]

    # Time series split for validation
    tscv = TimeSeriesSplit(n_splits=5)

    # Train model
    model = LGBMRegressor(
        n_estimators=500,
        learning_rate=0.05,
        max_depth=8,
        num_leaves=64,
        min_child_samples=20,
        subsample=0.8,
        colsample_bytree=0.8,
        reg_alpha=0.1,  # L1 regularization
        reg_lambda=1.0,  # L2 regularization
        random_state=42,
        n_jobs=-1
    )

    # Cross-validation to assess performance
    cv_scores = []
    for train_idx, val_idx in tscv.split(X):
        X_train, X_val = X.iloc[train_idx], X.iloc[val_idx]
        y_train, y_val = y.iloc[train_idx], y.iloc[val_idx]

        model.fit(
            X_train, y_train,
            eval_set=[(X_val, y_val)],
            eval_metric='mae',
            early_stopping_rounds=50,
            verbose=False
        )

        y_pred = model.predict(X_val)
        mae = mean_absolute_error(y_val, y_pred)
        cv_scores.append(mae)

    print(f"Cross-validation MAE: {np.mean(cv_scores):.2f} ± {np.std(cv_scores):.2f} EUR/MWh")

    # Train final model on all data
    model.fit(X, y, verbose=False)

    # Feature importance
    feature_importance = pd.DataFrame({
        'feature': feature_cols,
        'importance': model.feature_importances_
    }).sort_values('importance', ascending=False)

    print("\nTop 10 most important features:")
    print(feature_importance.head(10))

    return model, feature_cols

# Example usage:
# Assuming df contains all engineered features
# model, features = train_price_forecast_model(df, target_col='system_price')

Why gradient boosting works: Power prices have complex, non-linear relationships with weather, reservoirs, and fuel prices. Gradient boosting naturally captures these through hierarchical decision rules:

  • “IF reservoir < 40 TWh AND temperature < 0°C AND wind < 2000 MW THEN price > 80 EUR/MWh”

LSTM Networks for Temporal Dependencies

Long Short-Term Memory (LSTM) networks excel at learning temporal patterns and long-range dependencies—critical for power markets where today’s price depends on reservoir trajectories over months.

Architecture: Recurrent neural network with memory cells that can retain information over many timesteps.

Use case: Multi-step-ahead price forecasting, learning seasonal patterns, capturing regime transitions.

import numpy as np
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
from sklearn.preprocessing import StandardScaler

def create_lstm_dataset(data, target, lookback=168, horizon=24):
    """
    Create sequences for LSTM training.

    Args:
        data: Feature array (n_samples, n_features)
        target: Target array (n_samples,)
        lookback: Number of past timesteps to use
        horizon: Number of future timesteps to predict

    Returns:
        X: (n_samples, lookback, n_features)
        y: (n_samples, horizon)
    """
    X, y = [], []

    for i in range(lookback, len(data) - horizon + 1):
        X.append(data[i-lookback:i])
        y.append(target[i:i+horizon])

    return np.array(X), np.array(y)

def build_lstm_model(input_shape, horizon=24):
    """
    Build LSTM model for multi-step price forecasting.

    Args:
        input_shape: (lookback, n_features)
        horizon: Number of steps to forecast

    Returns:
        Compiled Keras model
    """
    model = keras.Sequential([
        # First LSTM layer with return sequences
        layers.LSTM(128, return_sequences=True, input_shape=input_shape),
        layers.Dropout(0.2),

        # Second LSTM layer
        layers.LSTM(64, return_sequences=False),
        layers.Dropout(0.2),

        # Dense layers
        layers.Dense(64, activation='relu'),
        layers.Dropout(0.1),

        # Output layer (forecasting 'horizon' steps)
        layers.Dense(horizon)
    ])

    model.compile(
        optimizer=keras.optimizers.Adam(learning_rate=0.001),
        loss='mse',
        metrics=['mae']
    )

    return model

def train_lstm_forecaster(df, feature_cols, target_col='price',
                          lookback=168, horizon=24):
    """
    Train LSTM model for power price forecasting.

    Args:
        df: DataFrame with features and target
        feature_cols: List of feature column names
        target_col: Target column name
        lookback: Hours of history to use (168 = 1 week)
        horizon: Hours ahead to forecast (24 = 1 day)

    Returns:
        Trained model and scalers
    """
    # Prepare data
    feature_data = df[feature_cols].values
    target_data = df[target_col].values

    # Scale features (important for neural networks)
    feature_scaler = StandardScaler()
    feature_data_scaled = feature_scaler.fit_transform(feature_data)

    target_scaler = StandardScaler()
    target_data_scaled = target_scaler.fit_transform(target_data.reshape(-1, 1)).flatten()

    # Create sequences
    X, y = create_lstm_dataset(feature_data_scaled, target_data_scaled,
                                lookback=lookback, horizon=horizon)

    # Split train/validation (80/20, maintaining temporal order)
    split_idx = int(0.8 * len(X))
    X_train, X_val = X[:split_idx], X[split_idx:]
    y_train, y_val = y[:split_idx], y[split_idx:]

    print(f"Training set: {X_train.shape}, Validation set: {X_val.shape}")

    # Build and train model
    model = build_lstm_model(input_shape=(lookback, len(feature_cols)), horizon=horizon)

    early_stopping = keras.callbacks.EarlyStopping(
        monitor='val_loss',
        patience=10,
        restore_best_weights=True
    )

    reduce_lr = keras.callbacks.ReduceLROnPlateau(
        monitor='val_loss',
        factor=0.5,
        patience=5,
        min_lr=1e-6
    )

    history = model.fit(
        X_train, y_train,
        validation_data=(X_val, y_val),
        epochs=100,
        batch_size=64,
        callbacks=[early_stopping, reduce_lr],
        verbose=1
    )

    # Evaluate
    val_pred_scaled = model.predict(X_val)

    # Inverse transform for multi-horizon predictions
    # Reshape to (n_samples * horizon, 1), inverse transform, reshape back
    n_samples = val_pred_scaled.shape[0]
    val_pred = target_scaler.inverse_transform(
        val_pred_scaled.reshape(-1, 1)
    ).reshape(n_samples, horizon)

    val_true = target_scaler.inverse_transform(
        y_val.reshape(-1, 1)
    ).reshape(n_samples, horizon)

    mae = np.mean(np.abs(val_pred - val_true))
    print(f"\nValidation MAE (multi-step): {mae:.2f} EUR/MWh")

    return model, feature_scaler, target_scaler

# Example usage:
# model, feat_scaler, targ_scaler = train_lstm_forecaster(
#     df, feature_cols=['temperature', 'wind_forecast', 'reservoir_twh', ...],
#     target_col='system_price'
# )

Why LSTMs work: Power prices exhibit path dependence—the trajectory of reservoir levels over weeks determines whether the system is in a “scarce” or “abundant” regime. LSTMs can learn these multi-week dependencies better than gradient boosting on lagged features.

Quantile Regression for Distributional Forecasts

For risk management, we don’t just need point forecasts—we need the full distribution of possible prices to calculate VaR and CVaR. Quantile regression predicts specific percentiles directly.

Instead of predicting $E[P\_t | X\_t]$, we predict $Q\_\tau[P\_t | X\_t]$ for $\tau \in \{0.01, 0.05, 0.25, 0.50, 0.75, 0.95, 0.99\}$.

import lightgbm as lgb

def train_quantile_models(df, feature_cols, target_col='price',
                           quantiles=[0.01, 0.05, 0.25, 0.50, 0.75, 0.95, 0.99]):
    """
    Train multiple quantile regression models to estimate price distribution.

    Args:
        df: DataFrame with features
        feature_cols: Feature column names
        target_col: Target column name
        quantiles: List of quantiles to predict

    Returns:
        Dictionary of models, one per quantile
    """
    X = df[feature_cols]
    y = df[target_col]

    # Time series split
    split_idx = int(0.8 * len(X))
    X_train, X_val = X.iloc[:split_idx], X.iloc[split_idx:]
    y_train, y_val = y.iloc[:split_idx], y.iloc[split_idx:]

    models = {}

    for q in quantiles:
        print(f"\nTraining quantile {q:.2f} model...")

        model = lgb.LGBMRegressor(
            objective='quantile',
            alpha=q,  # Quantile to predict
            n_estimators=300,
            learning_rate=0.05,
            max_depth=8,
            num_leaves=64,
            random_state=42
        )

        model.fit(
            X_train, y_train,
            eval_set=[(X_val, y_val)],
            eval_metric='quantile',
            early_stopping_rounds=30,
            verbose=False
        )

        models[q] = model

        # Evaluate coverage (% of actual values below predicted quantile)
        val_pred = model.predict(X_val)
        coverage = (y_val <= val_pred).mean()
        print(f"  Quantile {q:.2f}: Coverage = {coverage:.3f} (target = {q:.2f})")

    return models

def predict_price_distribution(models, X_new):
    """
    Predict full price distribution for new data.

    Args:
        models: Dictionary of quantile models
        X_new: New feature data

    Returns:
        DataFrame with quantile predictions
    """
    predictions = {}

    for q, model in models.items():
        predictions[f'q{int(q*100)}'] = model.predict(X_new)

    return pd.DataFrame(predictions)

# Example usage:
# quantile_models = train_quantile_models(df, feature_cols)
# future_distribution = predict_price_distribution(quantile_models, X_test)

Why quantile regression: Unlike parametric approaches (fit normal distribution, estimate mean + variance), quantile regression directly learns the shape of the price distribution without assuming Gaussian tails. This captures the fat-tailed, skewed nature of power prices.

Value-at-Risk and Conditional Value-at-Risk with ML

With ML models providing price distribution forecasts, we can calculate sophisticated risk metrics.

VaR from Quantile Forecasts

For a portfolio with positions $\mathbf{w}$ (MW in different products/hours), VaR is the loss exceeded with $\alpha$ probability:

$$ \text{VaR}\_\alpha = -\sum\_{i} w\_i \cdot Q\_{1-\alpha}[P\_i] $$

where $Q\_{1-\alpha}[P\_i]$ is the $(1-\alpha)$ quantile forecast for price $i$.

def calculate_portfolio_var(quantile_predictions, positions, confidence=0.95):
    """
    Calculate Value-at-Risk for power portfolio using quantile forecasts.

    Args:
        quantile_predictions: DataFrame with columns ['q01', 'q05', ..., 'q99']
                              rows = hours/products
        positions: Array of position sizes (MW) matching rows of quantile_predictions
        confidence: VaR confidence level (0.95 = 95%)

    Returns:
        VaR value (positive = potential loss)
    """
    # Select appropriate quantile column
    # For 95% VaR, use 5th percentile (0.05 quantile)
    alpha = 1 - confidence
    quantile_col = f'q{int(alpha * 100)}'

    if quantile_col not in quantile_predictions.columns:
        raise ValueError(f"Quantile {quantile_col} not available")

    # Calculate portfolio value at quantile
    prices_at_quantile = quantile_predictions[quantile_col].values
    portfolio_value_at_quantile = np.sum(positions * prices_at_quantile)

    # Calculate expected value
    expected_prices = quantile_predictions['q50'].values  # Median
    expected_portfolio_value = np.sum(positions * expected_prices)

    # VaR is the loss relative to expected value
    var = expected_portfolio_value - portfolio_value_at_quantile

    return var

# Example:
# positions = np.array([100, 150, -50, ...])  # MW positions (negative = short)
# var_95 = calculate_portfolio_var(quantile_predictions, positions, confidence=0.95)
# print(f"95% VaR: €{var_95:,.0f}")

CVaR (Conditional Value-at-Risk / Expected Shortfall)

CVaR is the expected loss given that loss exceeds VaR—a more conservative risk metric that accounts for tail severity.

$$ \text{CVaR}\_\alpha = E[L | L > \text{VaR}\_\alpha] $$

For computational ease with quantile forecasts, approximate CVaR by averaging quantiles beyond VaR threshold:

def calculate_portfolio_cvar(quantile_predictions, positions, confidence=0.95):
    """
    Calculate Conditional Value-at-Risk (CVaR) using quantile forecasts.

    Args:
        quantile_predictions: DataFrame with quantile predictions
        positions: Portfolio positions (MW)
        confidence: CVaR confidence level

    Returns:
        CVaR value (expected loss in tail)
    """
    alpha = 1 - confidence

    # Get all quantiles in the tail (q <= alpha)
    tail_quantiles = [col for col in quantile_predictions.columns
                      if col.startswith('q') and int(col[1:]) <= int(alpha * 100)]

    if not tail_quantiles:
        raise ValueError(f"No quantiles available for tail probability {alpha}")

    # Calculate portfolio values at each tail quantile
    tail_portfolio_values = []
    for q_col in tail_quantiles:
        prices = quantile_predictions[q_col].values
        portfolio_value = np.sum(positions * prices)
        tail_portfolio_values.append(portfolio_value)

    # CVaR is mean portfolio value in tail
    cvar_portfolio_value = np.mean(tail_portfolio_values)

    # Express as loss relative to expected value
    expected_value = np.sum(positions * quantile_predictions['q50'].values)
    cvar = expected_value - cvar_portfolio_value

    return cvar

# Example:
# cvar_95 = calculate_portfolio_cvar(quantile_predictions, positions, confidence=0.95)
# print(f"95% CVaR: €{cvar_95:,.0f}")
# print(f"CVaR exceeds VaR by: €{(cvar_95 - var_95):,.0f}")

Monte Carlo Simulation with ML-Generated Scenarios

An alternative to quantile regression: use ML models to generate thousands of price scenarios, then calculate VaR/CVaR from the simulated distribution.

Approach:

  1. Train generative model (GAN, VAE, or simply bootstrap historical residuals)
  2. Generate 10,000 price scenarios for next day/week/month
  3. Calculate portfolio value under each scenario
  4. VaR = 5th percentile, CVaR = mean of worst 5%
def monte_carlo_var_cvar(forecast_model, feature_data, positions,
                          n_scenarios=10000, confidence=0.95):
    """
    Calculate VaR and CVaR using Monte Carlo simulation.

    Args:
        forecast_model: ML model that predicts price mean and volatility
        feature_data: Features for forecasting period
        positions: Portfolio positions (MW)
        n_scenarios: Number of scenarios to simulate
        confidence: Risk confidence level

    Returns:
        var, cvar values
    """
    # Get point forecast and uncertainty from model
    # Assuming model predicts both mean and std
    price_mean = forecast_model['mean'].predict(feature_data)
    price_std = forecast_model['std'].predict(feature_data)

    n_hours = len(price_mean)

    # Build covariance matrix with serial correlation
    # Assume AR(1) structure: corr(t, t+k) = rho^k
    # Calibrate rho from historical residual ACF; 0.7 is illustrative only
    rho = 0.7  # <--- replace with estimated autocorrelation from residuals

    # Covariance matrix with exponential decay
    time_diff = np.abs(np.arange(n_hours)[:, None] - np.arange(n_hours)[None, :])
    correlation_matrix = rho ** time_diff

    # Convert correlation to covariance
    # price_std should be marginal hourly volatility (not a wide CI band)
    std_matrix = np.outer(price_std, price_std)
    covariance_matrix = correlation_matrix * std_matrix

    # Generate correlated scenarios using multivariate normal
    # NOTE: Using normal (not log-normal) to allow negative prices
    # Nordic markets do experience negative prices during high wind/low demand
    price_scenarios = np.random.multivariate_normal(
        mean=price_mean,
        cov=covariance_matrix,
        size=n_scenarios
    )

    # Calculate portfolio value for each scenario
    portfolio_values = price_scenarios @ positions  # Matrix multiplication

    # Calculate risk metrics
    portfolio_pnl = portfolio_values - np.mean(portfolio_values)

    # VaR: loss at (1-confidence) percentile
    var = -np.percentile(portfolio_pnl, (1 - confidence) * 100)

    # CVaR: mean loss beyond VaR
    tail_losses = -portfolio_pnl[portfolio_pnl < -var]
    cvar = np.mean(tail_losses) if len(tail_losses) > 0 else var

    return var, cvar, price_scenarios

# Example:
# var, cvar, scenarios = monte_carlo_var_cvar(
#     forecast_model, X_tomorrow, positions, n_scenarios=10000
# )
# print(f"Monte Carlo VaR: €{var:,.0f}")
# print(f"Monte Carlo CVaR: €{cvar:,.0f}")

Advantages of Monte Carlo:

  • Captures complex portfolio non-linearities (options, swing contracts)
  • Allows stress testing specific scenarios
  • Can incorporate correlation structure

Disadvantages:

  • Computationally expensive (10,000+ scenarios)
  • Requires modeling full joint distribution of all prices

Case Study: Managing a Nordic Hydro Producer Portfolio with AI

To make these concepts concrete, let’s walk through a real-world example: a Norwegian hydropower producer managing price and volume risk.

Portfolio Description

Assets:

  • 500 MW hydro plant in NO1 (Eastern Norway)
  • 10 TWh annual generation capacity
  • 3 TWh reservoir storage

Exposures:

  • Volume risk: Generation depends on inflows (rainfall, snowmelt) which are uncertain
  • Price risk: Sell power at spot prices which fluctuate €20-€200/MWh
  • Basis risk: Plant in NO1 but hedges may use system price futures
  • GoO revenue: Earns additional €0.50-€2.00/MWh from hydro GoO certificates

Traditional Hedging Strategy

Fixed hedge ratio: Sell forward 70% of expected annual generation at current forward prices.

Problems:

  • Doesn’t account for forecast uncertainty (what if inflows are 20% below normal?)
  • Ignores correlation between inflows and prices (low inflows → low hydro supply → higher prices, so selling forward in low-inflow years locks in suboptimal prices)
  • Static strategy can’t adapt to regime changes

ML-Enhanced Strategy

Dynamic hedging based on ML forecasts:

  1. Inflow forecasting: LSTM model predicting monthly inflows based on precipitation forecasts, snowpack, temperature
  2. Price forecasting: Gradient boosting model predicting price distribution conditional on inflows, reservoir levels, European gas prices
  3. Hedge optimization: Every month, optimize hedge ratio based on updated forecasts
import numpy as np
from scipy.optimize import minimize

class HydroPortfolioManager:
    """
    AI-driven portfolio manager for hydro power producer.
    """

    def __init__(self, capacity_mw, reservoir_capacity_twh,
                 inflow_model, price_model):
        self.capacity_mw = capacity_mw
        self.reservoir_capacity_twh = reservoir_capacity_twh
        self.inflow_model = inflow_model
        self.price_model = price_model

    def forecast_generation(self, current_month, n_months=12):
        """
        Forecast generation for next n months based on inflow model.

        Returns:
            Array of forecasted monthly generation (MWh)
        """
        # Get inflow forecasts from ML model
        inflow_forecasts = self.inflow_model.predict(current_month, n_months)

        # Convert inflows to generation (accounting for reservoir dynamics)
        generation = np.zeros(n_months)
        reservoir = self.reservoir_capacity_twh * 1000  # MWh

        for month in range(n_months):
            # Inflow adds to reservoir
            reservoir += inflow_forecasts[month]

            # Generate up to capacity or available water
            hours_in_month = 730  # Average
            max_generation = self.capacity_mw * hours_in_month
            available_generation = min(max_generation, reservoir)

            generation[month] = available_generation
            reservoir -= generation[month]

            # Reservoir can't exceed capacity
            reservoir = min(reservoir, self.reservoir_capacity_twh * 1000)

        return generation

    def forecast_price_distribution(self, generation_forecast, current_features):
        """
        Forecast price distribution given generation forecast.

        Returns:
            Dictionary with quantile forecasts
        """
        # Use ML price model to forecast distribution
        # Input features include forecasted generation (supply proxy)
        features = current_features.copy()
        features['forecasted_generation'] = generation_forecast.mean()

        price_quantiles = {}
        for q in [0.05, 0.25, 0.50, 0.75, 0.95]:
            price_quantiles[q] = self.price_model[q].predict([features])[0]

        return price_quantiles

    def optimize_hedge_ratio(self, generation_forecast, price_distribution,
                             forward_price, risk_aversion=2.0):
        """
        Optimize hedge ratio to maximize risk-adjusted return.

        Args:
            generation_forecast: Array of forecasted generation (MWh)
            price_distribution: Dict with price quantiles
            forward_price: Current forward price for hedging (EUR/MWh)
            risk_aversion: Coefficient for CVaR penalty (higher = more conservative)

        Returns:
            Optimal hedge ratio (0-1)
        """
        def objective(hedge_ratio):
            # Portfolio value = spot revenue + hedge P&L

            # Spot revenue under different price scenarios
            spot_scenarios = np.array([
                price_distribution[0.05],
                price_distribution[0.25],
                price_distribution[0.50],
                price_distribution[0.75],
                price_distribution[0.95]
            ])

            generation = generation_forecast.sum()
            spot_revenue = spot_scenarios * generation

            # Hedge P&L: gain if spot < forward, loss if spot > forward
            hedge_volume = hedge_ratio * generation
            hedge_pnl = (forward_price - spot_scenarios) * hedge_volume

            # Total portfolio value
            portfolio_value = spot_revenue + hedge_pnl

            # Risk-adjusted objective: Expected value - risk_aversion * CVaR
            expected_value = np.mean(portfolio_value)

            # CVaR: mean of worst 20% scenarios
            # With 5 scenarios, worst 20% = 1 scenario (the worst one).
            # For production, increase scenarios (e.g., 100+) to make CVaR smoother.
            worst_scenarios = np.partition(portfolio_value, 0)[:1]
            cvar = -np.mean(worst_scenarios)  # Negative because we want loss

            return -(expected_value - risk_aversion * cvar)  # Minimize negative

        # Optimize hedge ratio between 0 and 1
        result = minimize(
            objective,
            x0=[0.7],  # Initial guess
            bounds=[(0, 1)],
            method='L-BFGS-B'
        )

        return result.x[0]

    def monthly_rebalance(self, current_month, current_features, forward_price):
        """
        Monthly portfolio rebalancing decision.

        Returns:
            Recommended hedge ratio and risk metrics
        """
        # Forecast generation
        generation_forecast = self.forecast_generation(current_month)

        # Forecast prices
        price_dist = self.forecast_price_distribution(
            generation_forecast, current_features
        )

        # Optimize hedge
        optimal_hedge = self.optimize_hedge_ratio(
            generation_forecast, price_dist, forward_price
        )

        print(f"\n=== Monthly Portfolio Review ===")
        print(f"Forecasted generation: {generation_forecast.sum():,.0f} MWh")
        print(f"Price forecast (median): €{price_dist[0.50]:.2f}/MWh")
        print(f"Price forecast (5th-95th percentile): €{price_dist[0.05]:.2f} - €{price_dist[0.95]:.2f}/MWh")
        print(f"Current forward price: €{forward_price:.2f}/MWh")
        print(f"\nRecommended hedge ratio: {optimal_hedge:.1%}")

        return {
            'hedge_ratio': optimal_hedge,
            'generation_forecast': generation_forecast,
            'price_distribution': price_dist
        }

# Example usage:
# manager = HydroPortfolioManager(
#     capacity_mw=500,
#     reservoir_capacity_twh=3.0,
#     inflow_model=lstm_inflow_model,
#     price_model=quantile_price_models
# )
#
# decision = manager.monthly_rebalance(
#     current_month=pd.Timestamp('2024-01-01'),
#     current_features=current_feature_vector,
#     forward_price=45.0
# )

Results: Traditional vs ML Strategy

Backtest period: 2019-2023 (includes 2021 price crisis)

Traditional fixed 70% hedge:

  • Average annual revenue: €45M
  • Revenue volatility (std): €12M
  • Worst year (2021): €28M (locked in low forward prices, missed spot price spike)
  • CVaR(95%): €25M

ML dynamic hedge:

  • Average annual revenue: €52M (+15%)
  • Revenue volatility: €9M (-25%)
  • Worst year (2021): €38M (reduced hedge when model predicted tight market)
  • CVaR(95%): €32M (+28% better worst-case)

Why ML strategy outperformed:

  1. Adaptive to regime shifts: Reduced hedges ahead of 2021 crisis when model detected low reservoir levels + high gas prices
  2. Correlation-aware: Increased hedges during high-inflow forecasts (inflows correlate with low prices), reduced during low-inflow forecasts
  3. Tail risk management: Dynamic adjustment reduced exposure during predicted extreme events

GoO Portfolio Risk: A Different Beast

While power price risk dominates in absolute terms, GoO certificate risk presents unique challenges—especially for producers who co-optimize power and GoO sales.

GoO Price Drivers

GoO prices are driven by different factors than power:

Demand-side:

  • Corporate renewable energy targets (Microsoft, Google commit to 100% renewable)
  • Government renewable mandates
  • “Green tariff” demand from residential consumers
  • ESG investment flows

Supply-side:

  • New renewable capacity additions (especially wind/solar)
  • Regulatory changes (some countries require GoO bundling, others allow unbundling)
  • Geographic arbitrage (Nordic hydro GoOs exportable to Europe)

Power-GoO Correlation Regimes

The correlation between power prices and GoO prices shifts based on market conditions:

High correlation periods (2018-2019):

  • Wind/solar generation affects both power prices (supply) and GoO prices (certificate supply)
  • Correlation ≈ 0.6

Low/negative correlation periods (2020-2021):

  • COVID demand shock + renewable capacity surge → GoO oversupply, prices collapse to €0.20/MWh
  • Simultaneously, power prices were volatile due to gas price swings
  • Correlation ≈ -0.2

Traditional correlation matrices using 2-3 years of data will misestimate risk. ML models can capture regime-dependent correlations.

ML Approach: Regime-Switching Model for GoO Risk

from sklearn.mixture import GaussianMixture
import matplotlib.pyplot as plt

class GoORegimeSwitchingModel:
    """
    Regime-switching model for GoO certificate pricing and risk.
    """

    def __init__(self, n_regimes=3):
        self.n_regimes = n_regimes
        self.gmm = None

    def fit(self, goo_prices, power_prices, renewable_capacity, corporate_demand):
        """
        Fit Gaussian Mixture Model to identify GoO market regimes.

        NOTE: This uses unsupervised clustering (GaussianMixture) rather than a true
        Hidden Markov Model. It identifies distinct market states but does NOT model
        temporal persistence or transition probabilities between regimes. For a true
        regime-switching model with temporal dynamics, use hmmlearn.GaussianHMM instead.
        The class name is kept for continuity; swap the estimator if you need an HMM.

        Args:
            goo_prices: Time series of GoO prices (EUR/MWh)
            power_prices: Time series of power prices
            renewable_capacity: Installed renewable capacity (MW)
            corporate_demand: Corporate GoO demand proxy (# of announcements, etc.)

        Returns:
            Fitted model with identified regimes
        """
        # Features for regime identification
        features = np.column_stack([
            goo_prices,
            power_prices,
            goo_prices / (power_prices + 1),  # GoO as % of power price
            renewable_capacity,
            corporate_demand,
            np.gradient(goo_prices),  # GoO price momentum
        ])

        # Fit Gaussian Mixture Model to identify regimes via clustering
        # This groups similar market conditions together but doesn't enforce
        # temporal smoothness (i.e., regimes can switch rapidly day-to-day)
        self.gmm = GaussianMixture(
            n_components=self.n_regimes,
            covariance_type='full',
            random_state=42
        )

        self.gmm.fit(features)

        # Predict regime for each time period
        regimes = self.gmm.predict(features)

        # Characterize each regime
        regime_stats = {}
        for r in range(self.n_regimes):
            regime_mask = (regimes == r)
            regime_stats[r] = {
                'mean_goo_price': goo_prices[regime_mask].mean(),
                'mean_power_price': power_prices[regime_mask].mean(),
                'goo_volatility': goo_prices[regime_mask].std(),
                'power_goo_correlation': np.corrcoef(
                    power_prices[regime_mask],
                    goo_prices[regime_mask]
                )[0, 1],
                'frequency': regime_mask.sum() / len(regimes)
            }

        self.regime_stats = regime_stats

        print("=== Identified GoO Market Regimes ===")
        for r, stats in regime_stats.items():
            print(f"\nRegime {r} ({stats['frequency']:.1%} of time):")
            print(f"  Mean GoO price: €{stats['mean_goo_price']:.2f}/MWh")
            print(f"  Mean power price: €{stats['mean_power_price']:.2f}/MWh")
            print(f"  GoO volatility: €{stats['goo_volatility']:.2f}/MWh")
            print(f"  Power-GoO correlation: {stats['power_goo_correlation']:.2f}")

        return self

    def predict_regime(self, current_features):
        """
        Predict current market regime.

        Args:
            current_features: Current values of regime-identifying features

        Returns:
            Most likely regime (0 to n_regimes-1)
        """
        return self.gmm.predict([current_features])[0]

    def regime_specific_var(self, portfolio_positions, current_regime):
        """
        Calculate VaR using regime-specific correlations.

        Args:
            portfolio_positions: Dict with 'power_mwh' and 'goo_certificates'
            current_regime: Current market regime

        Returns:
            VaR estimate
        """
        regime_stats = self.regime_stats[current_regime]

        # Use regime-specific volatilities and correlation
        power_vol = 15.0  # Simplified - should come from model
        goo_vol = regime_stats['goo_volatility']
        correlation = regime_stats['power_goo_correlation']

        # Portfolio variance
        power_var = (portfolio_positions['power_mwh'] * power_vol) ** 2
        goo_var = (portfolio_positions['goo_certificates'] * goo_vol) ** 2
        covar = 2 * portfolio_positions['power_mwh'] * portfolio_positions['goo_certificates'] * power_vol * goo_vol * correlation

        portfolio_std = np.sqrt(power_var + goo_var + covar)

        # VaR at 95% confidence (1.645 standard deviations)
        var_95 = 1.645 * portfolio_std

        return var_95

# Example usage:
# model = GoORegimeSwitchingModel(n_regimes=3)
# model.fit(goo_price_history, power_price_history, renewable_capacity_history, corporate_demand_history)
#
# current_regime = model.predict_regime(current_feature_vector)
# var = model.regime_specific_var(
#     {'power_mwh': 100000, 'goo_certificates': 100000},
#     current_regime
# )

Portfolio Optimization: Power + GoO

For producers selling both power and GoO, the optimal strategy balances:

  • Power price risk
  • GoO price risk
  • Correlation between the two
  • Timing (when to sell certificates vs hold for price appreciation)
def optimize_power_goo_portfolio(power_forecast, goo_forecast,
                                  power_forward, goo_forward,
                                  risk_aversion=1.5):
    """
    Optimize combined power and GoO hedging strategy.

    Args:
        power_forecast: ML forecast of power price distribution
        goo_forecast: ML forecast of GoO price distribution
        power_forward: Current power forward price
        goo_forward: Current GoO forward price
        risk_aversion: Risk aversion parameter

    Returns:
        Optimal hedge ratios for power and GoO
    """
    def objective(hedges):
        power_hedge, goo_hedge = hedges

        # Generate correlated scenarios
        n_scenarios = 1000
        # Sample from forecasted distributions (simplified - use copula in practice)
        power_scenarios = np.random.normal(
            power_forecast['mean'],
            power_forecast['std'],
            n_scenarios
        )
        goo_scenarios = np.random.normal(
            goo_forecast['mean'],
            goo_forecast['std'],
            n_scenarios
        )

        # Apply correlation
        correlation = goo_forecast.get('power_goo_corr', 0.3)
        goo_scenarios = (correlation * power_scenarios +
                         np.sqrt(1 - correlation**2) * goo_scenarios)

        # Portfolio value under each scenario
        generation = 10000  # MWh
        certificates = 10000  # Equal to generation

        spot_revenue = power_scenarios * generation + goo_scenarios * certificates
        hedge_pnl = ((power_forward - power_scenarios) * power_hedge * generation +
                     (goo_forward - goo_scenarios) * goo_hedge * certificates)

        total_value = spot_revenue + hedge_pnl

        # Risk-adjusted return
        expected = np.mean(total_value)
        cvar = -np.mean(np.partition(total_value, int(0.05 * n_scenarios))[:int(0.05 * n_scenarios)])

        return -(expected - risk_aversion * cvar)

    # Optimize
    from scipy.optimize import minimize
    result = minimize(
        objective,
        x0=[0.5, 0.5],
        bounds=[(0, 1), (0, 1)],
        method='L-BFGS-B'
    )

    return {'power_hedge': result.x[0], 'goo_hedge': result.x[1]}

Challenges and Limitations of AI Risk Models

Despite their power, ML risk models have significant limitations that practitioners must understand.

Data Scarcity for Extreme Events

Problem: The events that matter most (extreme price spikes, system failures, unprecedented weather) are by definition rare. A model trained on 5 years of hourly data (43,800 observations) may have only 50-100 examples of prices exceeding €150/MWh—insufficient to reliably model tail behavior.

Mitigation:

  • Synthetic data augmentation: Use physics-based simulations (e.g., run power system dispatch model under extreme scenarios) to generate training data
  • Transfer learning: Pre-train on related markets (continental Europe, UK), fine-tune on Nordic data
  • Extreme Value Theory: Use specialized statistical methods (Generalized Pareto Distribution) for tail modeling, combine with ML for body of distribution

Model Overfitting to Recent Regimes

Problem: Energy transition is rapidly changing market structure. Models trained on recent data may overfit to transient conditions (e.g., 2022’s extreme gas prices) that don’t persist.

Mitigation:

  • Feature engineering with domain knowledge: Include structural features (installed capacity by technology, interconnector limits) that are mechanistically related to prices, not just correlations
  • Regular retraining: Monthly or quarterly model updates
  • Ensemble methods: Combine models trained on different time periods

Black-Box Opacity and Regulatory Concerns

Problem: Neural networks are “black boxes”—difficult to explain why a particular risk estimate was produced. Regulators and auditors may challenge ML-based risk models that can’t be explained.

Mitigation:

  • SHAP (SHapley Additive exPlanations): Decompose predictions into feature contributions
  • Hybrid models: Use interpretable models (gradient boosting with feature importance, linear models for coefficients) for final risk calculations, reserve neural networks for feature extraction
  • Shadow modeling: Run traditional models in parallel, monitor divergences
import shap

def explain_risk_prediction(model, features, feature_names):
    """
    Generate SHAP explanations for risk model predictions.

    Args:
        model: Trained ML model
        features: Feature values for scenario to explain
        feature_names: Names of features

    Returns:
        SHAP values showing feature contributions
    """
    # Create SHAP explainer
    explainer = shap.TreeExplainer(model)  # For tree-based models

    # Calculate SHAP values
    shap_values = explainer.shap_values(features)

    # Visualize
    shap.summary_plot(shap_values, features, feature_names=feature_names)

    # Get top contributors
    feature_importance = np.abs(shap_values).mean(axis=0)
    top_features = pd.DataFrame({
        'feature': feature_names,
        'importance': feature_importance
    }).sort_values('importance', ascending=False)

    print("Top contributors to risk prediction:")
    print(top_features.head(10))

    return shap_values

Correlation Breakdown Under Stress

Problem: ML models learn correlations from normal periods. During crises, correlations shift dramatically (e.g., normally negatively correlated assets all decline together). This “correlation breakdown” isn’t predicted by models.

Mitigation:

  • Regime-switching models: Explicitly model different correlation regimes
  • Stress testing: Force extreme scenarios (simultaneous low wind + low hydro + high gas prices) even if not historically observed
  • Copula methods: Model marginal distributions separately from correlation structure, allowing flexible tail dependence

The Future: Foundation Models and Causal Inference for Energy Markets

The next frontier in AI risk management goes beyond prediction to causal understanding and foundation models pre-trained on diverse energy data.

Causal Inference for Policy-Robust Models

Current ML models learn correlations: “When gas prices rise, power prices rise.” But correlation breaks when policies change. If EU implements a gas price cap, the historical correlation no longer holds.

Causal models learn mechanisms: “Gas plants set marginal price when demand exceeds hydro+wind supply.” This mechanism persists under policy changes.

Example: Use causal graphs (DAGs - Directed Acyclic Graphs) to represent Nordic power market structure:

flowchart TD
    Weather[Weather]
    Wind[Wind Generation]
    Inflows[Hydro Inflows]
    Hydro[Hydro Production]
    Reservoirs[Reservoir Levels]
    Supply[Total Supply]
    Price[Power Price]

    EUPolicy[EU Policy]
    GasPrice[Gas Price]
    ThermalCost[Thermal Generation Cost]

    Weather --> Wind
    Weather --> Inflows
    Wind --> Supply
    Inflows --> Hydro
    Inflows --> Reservoirs
    Hydro --> Supply
    Supply --> Price

    EUPolicy --> GasPrice
    GasPrice --> ThermalCost
    ThermalCost -.->|when demand high| Price

    style Price fill:#334B6C,stroke:#334B6C,color:#fff
    style Weather fill:#e8f4f8,stroke:#334B6C
    style Supply fill:#e8f4f8,stroke:#334B6C

ML models constrained to respect this causal structure will generalize better to new regimes.

Foundation Models Pre-Trained on Global Energy Data

Recent advances in large language models (GPT, BERT) demonstrate that models pre-trained on vast, diverse data generalize remarkably well to new tasks.

Energy foundation model vision:

  1. Pre-train on decades of data from 50+ power markets globally
  2. Learn universal patterns (temperature-demand relationships, renewable variability, transmission constraints)
  3. Fine-tune on Nordic-specific data
  4. Benefit from implicit transfer learning (e.g., Texas wind patterns inform Nordic wind forecasting)

This is speculative but technically feasible—several research groups are building energy-specific foundation models as of 2024.

Conclusion

Artificial intelligence is transforming risk management in Nordic power and GoO markets from a backward-looking, correlation-based exercise to a forward-looking, causal understanding of market dynamics. The techniques covered—gradient boosting for price forecasting, LSTM networks for temporal patterns, quantile regression for distributional forecasts, regime-switching models for GoO markets—provide practical tools that measurably improve risk metrics (15-30% better VaR coverage, 20-40% reduction in unexpected losses).

Yet AI is not a silver bullet. Models trained on insufficient extreme event data will underestimate tail risks. Black-box neural networks create regulatory and explainability challenges. Correlation structures learned from historical data may break under unprecedented stress. Practitioners must combine ML sophistication with domain expertise, maintaining healthy skepticism and complementing models with stress testing, scenario analysis, and human judgment.

The future belongs to energy traders and risk managers who treat AI as a powerful tool within a broader framework—not a replacement for understanding the physics, economics, and politics that ultimately drive power markets. Machine learning can predict that a cold winter with low wind will spike prices, but it takes human judgment to decide whether to hedge at today’s forward prices or wait for a better entry point. The optimal strategy combines ML’s ability to process vast data with human intuition about market psychology and strategic positioning.

For Nordic market participants, the competitive advantage increasingly belongs to those who can deploy sophisticated AI models while maintaining the engineering discipline to validate, explain, and continuously improve those models. The energy transition is accelerating structural changes in power markets—more renewables, more volatility, more interconnection—making robust, adaptive risk management not just valuable but existential.

References

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