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Monte Carlo Valuation of Renewable Power Options with Capture and Volume Risk

Article Quant Q&A · Author: CasusBelli
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Summary

The document considers valuing a monthly option on a renewable asset’s generation-weighted power price. It cautions that shaping a hub futures contract and applying Black–76 may miss important risks, especially when settlement depends on actual production. The response separates baseload price uncertainty, capture-factor uncertainty associated with cannibalization, and production-volume uncertainty. It proposes modeling baseload prices and capture factors separately, then combining them in simulated outcomes; stochastic production volumes can also be included when the contract requires them.

Because the product of a lognormal price and a normally distributed capture factor does not follow the standard Black–76 lognormal assumption, the response recommends Monte Carlo valuation, potentially with two-factor models calibrated to volatility term structures. Simulated option payoffs are weighted by production volume and averaged. This is a conceptual framework, not a complete calibration recipe: the document gives no parameter estimates, validation results, or detailed model specification, and the appropriate setup depends on the contract’s settlement terms.

Key ideas

  • Renewable power option valuation may involve price, capture-factor, and production-volume uncertainty.
  • A shaped futures price alone may not represent the payoff distribution for a pay-as-produced contract.
  • The product of lognormal baseload prices and normally distributed capture factors does not satisfy Black–76’s standard distribution assumption.
  • Monte Carlo simulation can combine price, capture-factor, and volume scenarios to estimate option payoffs.
  • Model inputs and calibration should reflect the option’s actual settlement definition.

Tags

OptionsCommoditiesVolatilityDerivatives pricing
Full text
# Black 76 and Asian Style Options on Shaped Power Futures


# Black 76 and Asian Style Options on Shaped Power Futures












I am attempting to price a monthly lookback option on the gen-weighted average price of power at a particular solar plant over a given month. If the option settles at hub H, am I right to shape the corresponding's month's futures contract with the asset's generation profile, and then using the resulting shaped contract as my F and the volatility of the shaped contract as my V in the Black-76 equation?

## Answer by ZRH (score 2)

https://quant.stackexchange.com/a/76433

I think to answer your question, it needs to be understood accurately how the option contract that you are pricing is defined. If you are looking at a pay-as-produced type option, you also need to factor in volume uncertainty. Overall, you are looking at three types of uncertainty for solar and wind assets:

- Price uncertainty (on baseload), as inferred historically or from options data

- Cannibalization uncertainty

- Volume uncertainty

An elegant way to circumvent the shaping that you suggest is to firstly model baseload prices, and to then multiply baseload prices with capture factors (100% - cannibalization in %age terms). Doing so, the effectively realised price is given by the product of baseload price and capture factor.

That said, using Black76 is not accurate as capture factors are normally distributed, whereas prices are lognormally distributed. In other words, the effective prices obey the distribution of a product of normal and lognormal random variables, which is not an analytical distribution. It is therefore better to run Monte-Carlo simulations, typically using two-factor models calibrated to the term structure of volatilities.

Further, if your option contract is intended to reference stochastic production volumes, you need to also calibrate volume uncertainty (cf above point 3). The undiscounted value of eg a call option in simulation scenario $i$ is thus (where $p_{base}$ is baseload price, $cf_i$ is capture factor, $q_i$ is the production volume, $K$ is the strike price)

$Call=\frac{1}{N}\sum_{i=1}^N max(p_i cf_i-K,0) q_i$

This method is quite elegant since it avoids the complications of hourly production shaping consistent with expected cannibalization, and further it is very versatile for modeling RES assets, irrespective of whether they are solar or wind.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.