Module forward_start_option 

Forward-start options: the strike is fixed at a future date t_f as a fraction k of the then-prevailing spot; the payoff at expiry T is (S_T - k * S_{t_f})^+ (call) or the mirrored put.

• Black-Scholes closed form (Rubinstein 1991) via homogeneity: price = S_0 e^{-q t_f} * BS(1, k, r, q, sigma, T - t_f).
• Monte Carlo through Payoff::path_payoff: the payoff reads S_{t_f} off the simulated path, so the option prices under GBM, local vol and — the reason this product exists — Heston stochastic vol, whose forward smile differs materially from Black-Scholes.

Structs

ForwardStartPayoff

Functions

forward_start_price

Rubinstein closed form under Black-Scholes: by homogeneity the value at the fixing date is S_{t_f} * BS(1, k, r, q, sigma, T - t_f), so the time-0 value replaces S_{t_f} by its dividend-discounted spot.