A forward start option is an option that comes into existence at some future time T₁ and expires at T₂ (T₂ > T₁). The strike price is set equal the asset price at T₁ such that the option is at-the-money at the future option’s initiation time T₁. Consider a forward start call option whose underlying asset has value S at current time t and constant dividend yield q, show that the value of the forward start call is given by

where c(S,T₂ − T₁; S) is the value of an at-the-money call (strike price same as asset price) with time to expiry T₂ − T₁.

The value of an at-the-money call option is proportional to the asset price.

Transcribed Image Text:

e-91c(S, T₂-T1; S),