FSMA – 6055 Financial Derivatives H W # 5 Considering the information provided in the question then: u = 1+60% = 1.60, d = 1- 37.5% = 0.625, R = 1.06 (6% annual compounding rate), t = 1 year Therefore, up movement Risk neutral probability: p = (R-d)/(u-d) = (1.06-0.625)/(1.6-0.625) = 0.446154. Hence q = 1-p = 0.553846 The lattice of stock and value of $100 call and put at expiry is as below: 409.6309.60 256160600 16010062,5037.510062.539.062524.414063075.58594t=0t=1t=2t=3Value of call at t=3Value of put at t=3 (1) Suppose it is European call option: (p^3*value of call at t=3 at price $409.60+3*p^2*q*value of call at t=3 at price $160+3*q^2*p*value of call at t=3 at price $62.5+q^3*value of call at t=3 at price $24.414)/R^3 = (0.446154^3*309.6+3*0.446154^2*0.553846*60+0+0)/1.06^3 = 39.74689 Hence the value of European call option = $39.75 (2) Suppose it is European put option: (p^3*value of put at t=3 at price $409.60+3*p^2*q*value of put at t= 3 at price $160+3*q^2*p value of put t=3 at price $62.5+q^3* value of put at t=3 at price $24.414)/R^3 = (0+0+3*0.446154*0.553846^2*37.5+0.553846^3*75.58594)/1.06^3 = 23.708 Hence the value of European put option = $23.71 (3) Suppose it is American put option: The value of American put option at t = 2 at stock price $256: max{100-256, (p*value of put at t=3 at price $409.6+q*value of put at t=3 at price $160)/R} = max{-156,(0.446154*0+0)/1.06} = 0 The value of American put option at t=2 at stock price $100: max{100-100, (p*value of at t=3 at price $160+q*value of put at t=3 at price $62.5)/R} = max{0, (0+0.553846*37.5)/1.06} = $19.5936 The value of American put option at t=2 at the price of $39.0625: max{100-39.0625, (p*value of put at t=3 at price $62.5+q* value of put at t=3 at price $24.41)/R} = max{60.9375,(0.446154*37.5+0.553846*75.58594)/1.06} = max(60.9375,55.277) = $60.9375 – Here early exercise is optimal The value of American put option at t=1 at stock price of $160: max{100-160,(p*value of put at t=2 at price $256+q*value of put at t=2 at price $100)/R} =max{-60,(0.446154*0+0.553846*19.5936)/1.06} =max(-60,10.237582) = $10.237582 The value of American put option at t=1 at stock price of $62.50: max{100-62.50,(p*value of put at t=2 at price $100+q*value of put at t=2 at price $39.0625)/R} =max{37.50,(0.446154*19.5936+0.553846*60.9375)/1.06} = max(37.50,40.08656) = $40.08656 The value of American put option at t=0 at stock price of $100: max{100-100,(p*value of put at t=1 at price $160+q*value of put t=1 at price $62.50)/R} = max{0,(0.446154*10.237582+0.553846*40.08656)/1.06} =max(0,25.254075) =$25.25 The value of American put option is therefore $25.25

- Assignment status: Already Solved By Our Experts
*(USA, AUS, UK & CA PhD. Writers)***CLICK HERE TO GET A PROFESSIONAL WRITER TO WORK ON THIS PAPER AND OTHER SIMILAR PAPERS, GET A NON PLAGIARIZED PAPER FROM OUR EXPERTS**

**NO PLAGIARISM**– CUSTOM PAPER