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(iii) Both the call option and put option will expire in 4 years. ... We are given that C - P = 0.15, S0 = 60, K = 70 and T = 4. Then ... Finally, discount and average Pu and Pd to get the time-0 price, ... d2 = d1 - σ√T = 0.2125 - 0.05/2 = 0.1875. ... t∂. ∂. = 0. If f(x) = ln x, then f ′(x) = 1/x and f ″(x) = -1/x2. Hence,.

Typically ∂σ∗∂k < 0 (the smile slope downwards) and the fair value of the digital ... higher than the 1/ √ 3 ≈ 0.577 proxy rule mentioned in Section 12-1.2 p.127. ... (a) This payoff corresponds to a 5-year zero-coupon bond worth e−2.5%×5 ...