Monte Carlo VaR for Correlated Energy Generation and Forward Prices
Summary
The document proposes estimating portfolio profit distributions by simulating monthly generation for each energy asset and electricity forward prices, multiplying generation by price to estimate asset revenues, summing across assets, and taking lower-tail quantiles for one-month risk over a multi-month horizon. It describes fitting separate distribution families to each asset’s generation and ARIMA models to forward price levels, based on roughly forty observations per asset-month and contract.
The author recognizes that independent simulations would omit dependence among assets, between generation and prices, across contract maturities, and across successive months. Those relationships matter because they can change portfolio tail outcomes. The document raises the issue but does not provide a dependence model, validation, or simulation results. Its short samples, distinct asset distributions, seasonal behavior, and changing futures liquidity near expiry are practical limits; the proposed workflow is therefore a starting point whose joint distributions and horizon assumptions need further specification.
Key ideas
- Monte Carlo simulation can combine uncertain generation and forward prices to estimate portfolio profit quantiles.
- Generation may require asset- and month-specific distribution models when its empirical behavior differs across sites.
- Modeling forward price levels with ARIMA does not by itself determine their joint dependence with generation or other contracts.
- Dependence across assets, prices, and months can materially affect simulated portfolio tail risk.
- Short histories and liquidity changes near contract expiry limit confidence in fitted distributions and forecasts.
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Full text
# Simulated VaR with differently distributed processes # Simulated VaR with differently distributed processes I am attempting to calculate the one-month 95th and 99th percentile profits for a two-year portfolio of energy-generating assets over the next three months. This means that the calculation has two components: 1) monthly electricity generation during the aforementioned two-year span and 2) energy futures prices (for each month in the two aforementioned year span). My analysis to date has shown that: a) the generation of each asset follows its own distribution family (based on minimizing the sum of square errors between empirical percentiles and theoretical distribution percentiles) and b) electricity forward prices (not their returns!) for the energy markets follow ARIMA models with significant variables, significant residual normality, insignificant residual autocorrelation, and insignificant heteroskedasticity. I have ~40 observations per month per electricity-generating asset and about 40 observations per electricity contract (liquidity increases substantially during the final 2 months, or 40 trading days, of an electricity contract -- which substantially changes its behavior) I propose: - Running N energy generation simulations per month per asset - Simulating N electricity forward prices per month - Taking the product of (1) and (2) - Summing (3) across all assets - Taking the desired quantile (either q=0.05 or q=0.01) of (4) Is this approach sound? Generation data are decidedly non-normal (even with the help of Box-Cox transformations and/or standardization and/or differencing) and seasonal (mean reverting at the monthly level) and different sites have starkly different distributions (e.g., Normal, Laplace, Levy, Johnson's Bounded, Cauchy) across months, so I've ruled out simpler VaR approaches like variance-covariance and historical VaR. I am hesitant because it does not explicitly account for correlation among: a) assets, b) between an asset and its respective forward price, or c) prices of successively expiring forward contracts, or d) generation of successive months. Your help and time are immensely appreciated!
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