Suppose there is a risky asset S and a risk-free asset B. On the second day,...

 

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Suppose there is a risky asset S and a risk-free asset B. On the second day, the risky asset dSo with probability 1 - p. Let r be the = will be worth S₁ = uSo with probability p and S₁ constant risk-free interest rate. (a) Let Po be the "no-arbitrage" (fair) price of a put option with strike K; and let Co be the "no-arbitrage" (fair) price of a call option with strike K. Prove the put-call parity: Co-Po So K 1+r (b) Suppose you observe that the market trading price of a call option with strike K is less than the "no-arbitrage" price Co. If you believe the model, how do you arbitrage from this? Suppose there is a risky asset S and a risk-free asset B. On the second day, the risky asset dSo with probability 1 - p. Let r be the = will be worth S₁ = uSo with probability p and S₁ constant risk-free interest rate. (a) Let Po be the "no-arbitrage" (fair) price of a put option with strike K; and let Co be the "no-arbitrage" (fair) price of a call option with strike K. Prove the put-call parity: Co-Po So K 1+r (b) Suppose you observe that the market trading price of a call option with strike K is less than the "no-arbitrage" price Co. If you believe the model, how do you arbitrage from this?

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Answer a To prove the putcall parity we start with the basic definitions of the call and put options Call option C This gives the holder the right but not the obligation to buy the risky asset 5 at th... View the full answer