I have a two-stage problem:
(1) Given market forwad curves and current implicit volatilities, value an implicit exotic option for a contract where the buyer agrees to purchase a commodity at price: max{M_i, D_i}_i - K, where K is a constant and M_i and D_i are monthly and daily indices for such commodity at day i, respectively (M_i changes value every 21+ workdays, say). Every month, M_i takes the value of the average of D_i over the last 5 days of the previous month.
(2) Provided a solution for (1), replicate it for simulated future price and volatility scenarios, generating a distribution of future prices of the implicit option.
Is there a standard way to solve (1), as an extension of the Black-Scholes model, for instance? If so, is it analytically equivalent to the expected payoff of the option simulated under the assumption that D_i behaves as a geometric brownian motion, with similar volatilities and mean price?
