Consider two dates T1, T2 with 0

Consider two dates Tl, T2 with 0 < Tl < T2. A forward start option is a contract in which the holder receives at time Tl, at no extra cost, an option with expiry date T2 and strike price equal to STI (the underlying asset price at Tl). Assume that the asset price evolves according to a two-period binary model, in which the asset price at time Tl is either Sou or Sod, and at time T2 is one of Sou2, Soud and Sod2 with TTI max{e rT1 d < min{e where r denotes the risk-free interest rate. (a) Determine the value of such a forward start call option at time zero. (b) Determine the value of such a forward start put option at time zero.