Question

A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum for all maturities and the dividend yield on the index is 2.5% (both continuously compounded). Calculate values for u, d, and p when a 6-month time step is used. What is value of a 12-month European put option with a strike price of 1,480 given by a two-step binomial tree?

In the question above, what is the value of a 12-month American put with a strike price of 1,480 given a two-step binomial tree?

Answer 1

• First 6 Months
• U = 1500*118%/1500 = 1.18
• D = 1500*82%/1500 = 0.82
• P = R-d/u-d = 1.02 - 0.82/1.18-0.82 = 0.56
• Next 6 months
• U = 2089/1770 = 1.18
• D= 1451/1770 = 0.82
• P = 1.02 - 0.82/1.18-0.82 = 0.56
• Value of European Option = 12.27*0.56 + 215.05*0.44/1.02 = 99.50
• In Case of American Put Option, we have to compare Discounted Value & Intrinsic Value
• Value = 0*.56+29*0.44/1.04 = 12.27, IV = 0 S>E
• Value = 0.56*29+0.44*471.4/1.04 = 215.05, IV = 230(1480 - 1230), So higher should be taken i.e, 230.
• Value of Option = 12.27*0.56+230*0.44/1.02 = 110.23