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A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per...

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?

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Expert Solution

GIVEN Strike price X 1480
Current stock price S 1500
Risk free interest rate per annum Rf 4%
Dividend yield dy 2.50%
Length of time step (in years) n1 0.5 square root = 0.707106781
Volatility σ 18%
COMPUTED Up factor u e to the power (σ*square root of n) e to the power (G8*I7)                                                           1.136
down factor d 1/u 1/I9                                                             0.88
probability (up) p e to the power (Rf-dy)*nn-d)/(u-d)                                                         1.0075          0.498
probability (down) 1-p          0.502
1934.8379 (put premium = IF (G3-J16>0,(G3-J16),0) 0
                                                 1,703.60 Put premium = 0 0
Stock price 1500 1500 put premium = 0 0
put premium=                                              242.18                                                  1,320.73 Put premium = 277.13                                                         159.27
1162.8881 put premium = 1480-1162 317.11188
put price                                                244.01 279.21
1.007528195 1.00753
ANSWER                                                242.18 277.13
put price formula (0*1.136+277.13*0.88)/dividing factor (0*1.136+0*0.88)/dividing factor
dividing factor e to the power (Rf-dy)*n e to the power (Rf-dy)*n

jeff jeffy answered 1 year ago
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