A forward start option is a derivative that gives the holder an option at a future date,

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Question:

A forward start option is a derivative that gives the holder an option at a future date, with strike price equal to the stock price on that date and maturity date given by a later date. For example, if a forward start European call specifies two future dates T1 and T2 with T1 < T2, then at time T1 the holder receives a European call with strike price ST1 and maturity date T2.

Compute the time-0 price of this forward start European call in a Black-Scholes-Merton economy.