Reference no: EM13940302
1. Use the Put-Call parity and the Black-Scholes formula for the European call from Proposition 1 to derive a similar formula for the European put option.
2. Hedging a long position:
Consider a bank that has a long position in a European Put written on the stock price in a one period binomial model with u = 2, v = ½, S = S0 = 4, and r = 1/16. The Put expires at time T = 1 and has strike price K = 3. At time zero, the bank owns this option, which ties up capital V0. The bank wants to earn the interest rate 6.25% on this capital until time one (i.e. "no matter what the markets do", the bank wants to have 1.0625 • V0 at time one). Specify how the bank's trader should invest in the stock and money markets to accomplish this.
3. Lookback option:
Suppose as in the Excel-File a three-period binomial model with u = 2, v = ½, S0 = 4, and r = 1/16. Consider a lookback option that pays off
V3 = max0≤n≤3 Sn - S3
at time three. Compute
(a) V0 and ?0;
(b) V1 and ?1.
4. American Puts, Calls, and Straddles:
Suppose as in the Excel-File a three-period binomial model with u = 2, v = ½ , S0 = 4, and r = 1/16.
(a) Determine the price at time zero, denoted V0P, of the American put that expires at time three and has intrinsic value gP(s) = (4 - s)+.
(b) Determine the price at time zero, denoted V0C, of the American call that expires at time three and has intrinsic value gC(s) = (s - 4)+.
(c) Determine the price at time zero, denoted V0S , of the American straddle that expires at time three and has intrinsic value gS(s) = gP(s) + gC(s).
(d) Explain why it is possible that V0S < V0P + V0C.
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