Question

Question 4 (25%) West's current stock price is $200. The price may rise to $230 or fall to $170 in one month. The risk-free interest rate is 18% per year. a. Using the replication portfolio approach, determine the price of a call on West's stock with an exercise price of $210 and one month maturity. b. If the stock price will either increase $50 or decrease $56 in month 2, using the risk neutral approach, calculate the price of a 2-month put option on West's stock that has an exercise price of $217.

Answer 1

a) Replication Portfolio Model Option Valuation West's Stock Current Price/Spot Price (S) Upper Future Spot Price (FSP) Lower Future Spot Price (FSP) Exercise Price/Strike Price (X) Risk Free Rate of Interest (Rh Maturity 200.00 230.00 170.00 210.00 1.5% per month 1 month (18%/12)

Steps a Present Value of Lower FSP =Lower FSP/(1+Ri^n =170/(1.015)^1 167.49 (n=number of periods/months) S( - ) Present Value of Lower FSP -200-167.49 32.51 Upper FSP ( - ) Lower FSP =230-170 60.00 (-) Call Option Value @ Upper FSP Call Option Value @ Lower FSP =170-210 =230-210 20.00 (-) 20.00 When FSP is less than X call option lapses. Therefor option value at lower FSP is 0 Find Levered Portfolio = c/d =60/20 3.00 Find Value of Call =b/e =32.51/3 10.84

b) Risk Neutral Model Option Valuation 200.00 250.00 West's Stock Current Price/Spot Price (S) Upper Future Spot Price (FSP) Lower Future Spot Price (FSP) Exercise Price/Strike Price (X) Risk Free Rate of Interest (RA) Maturity (200+50) (200-56) 144.00 (18%/12) 217.00 1.5% per month 2 month

Steps Find Risk Neutral Probability (P) It is the probability of Upper FSP P- FVF (-) u(-) d FVF = Future Value Factor =(1+RA)n =1.01542 1.03 Lower FSP =144/200 0.72 u= Upper FSP =250/200 1.25 0.59 1.03(-) 0.72 1.25 ( - ) 0.72

Find 1(-)P Probability of Lower FSP =1 (-) 0.59 0.41 find put option value at Upper FSP and Lower FSP Put option Value Upper FSP =217( - ) 250 Put option lapses When FSP is greater than X Put option Value Lower FSP 217( - ) 144 73.00 Expected Value of Put option P* Value @ Upper FSP (+)(1-P) * Value @ Lower FSP =(0.59*0) + (0.41*73) 29.93 The value found above is Future Vale. Discount it to today to find current Value of Put option =29.93/(1.015)^2 29.05