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A forward start options is an option where the exercise price isn't set till a date in the future.
They are sometimes used for employee stock options (ESO) where an employee is given a series of options with different maturity dates, but the strikes are all set in the future.
Once the strike is set on a forward start option they can be priced as a normal option. Details on pricing prior to the strike being set are below.
Forward start options can be priced using the Rubinstein (1990) formula:
c = Price of European call
p = Price of European put
S = The spot of the underlying asset
b = The cost of carry
r = The risk free rate
T = Time to expiry of the option
t = Elapsed time
N = The cumulative normal distribution function
= a positive constant, where the strike = S
= Volatility of underlying asset's price
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