# 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?

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:

1. Price uncertainty (on baseload), as inferred historically or from options data
2. Cannibalization uncertainty
3. 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.