Consider the 2-period Cox-Ross-Rubinstein (CRR) binomial model with S0 = K = 1, T = 1, ∆t = 0.5, σ = 0.2, u = 1/d = exp(σ √ ∆t), and continuously compounded interest rate r = 0.05. (a) State the martingale property of discounted underlying asset prices, and derive the CRR risk-neutral probabilities ˜p, and ˜q = 1 − p˜. (a) For both call and put options, calculate the price V0 and the initial replicating portfolio (ϕ (B) 0 , ϕ(S) 0 ). (b) Compare the signs of the delta hedging value ϕ (S) 0 for call and put options. Comment. (c) Now with σ = 0.4, re-calculate the price and delta hedging strategy of a call option. (d) Graph the discounted profit of the call options, defined as exp(−rT)VT − V0, for σ ∈ {0.2, 0.4}. Compare and comment on pricing and hedging differences.

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a Martingale Property In a riskneutral world the expected discounted future value of a... View the full answer