Question

The current price of Bank of America (BAC) is $10.The annual stan- dard deviation is 12%. The continuously compounded risk-free rate is 5% per year. Assume BAC pays no dividends. Compute the value of a 1 year European put option with a strike price of $7 using a one-period (At = 1 ) binomial model. (a) Compute the value of a 1 year European put option with a strike price of $7 using a one-step (At = 1) binomial model. (b) Compute the value of a 1 year European put option with a strike price of $7 using a two-step (At = 0.5 ) binomial model. (c) Compute the value of a 1 year European put option with a strike price of $7 using a three-step (At = 0.25 ) binomial model. (d) Compute the value of a 1 year European put option with a strike price of $7 using a four-step (At = 0.125 ) binomial model. (c) Compare the option prices from (a), (b), (c), and (d). What are your findings?

Answer 1

Risk Free Rate factor= e^(5%)=1.051

Upward price factor=1+12%=1.12

Downward price factor=1-12%=0.88

Probability of upward price=(R-d)/(u-d)=(1.051-0.88)/(1.12-0.88)=71.25%

Probability of downward price=1-71.25%=28.75%

Upward price after 1 year= 7*(1+12%)=7.84

Downward price after 1 year=7*0.88=6.16

call option payoff after 1 year= (7.84-7)*71.25%+0=0.5985

Present value of expected payoff= 0.5985/1.051=0.5694

Hence, value of european call option is 0.5694 as per one step binomial model.