30 points) Under the standard stock price model: dS(t) = rS(t)dt + σS(t)d ˜W (t), a. Derive the price of an option which

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30 points) Under the standard stock price model: dS(t) = rS(t)dt
+ σS(t)d ˜W (t), a. Derive the price of an option which pays 1 TL
at time T if S(T) ≥ K1 and pays 2 TL if S(T) > K2, where 0 <
K1 < K2 are two given strike prices. b. Find the delta hedge for
the option. c. Obtain numerical values for parts (a) and (b) when
S(0) = 100, T = 1 year, r = 0.2, σ = 0.3, K1 = 130 and K2 =
160.