Question

3. Use a one step binomial option pricing model to value a 1 year at the money call option on AT&T. Assume interest rates are 2 %. How does your value compare with the market price?

standard deviation is 15% and stock price is 50

exercise price is 50

Answer 1

Risk free rate factor (R)=1+2%=1.02

Upward price factor(u)= 1+15%=1.15

Downward price factor(d)=1-15%=0.85

Probability of upward price =(R-d)/(u-d)=(1.02-0.85)/(1.15-0.85)=56.67%

Probability of downward price=1-56.67%=43.33%

Upward Price after 1 year=50*1.15=57.5

Downward price after 1 year=50*0.85=42.5

Expected call option payoff= (57.5-50)*56.67%+0*43.33%=$4.25

Present value of expected payoff=4.25/1.02=$4.17(approx)

Hence, value of call option is $4.17

The current price of the share is around $37 and hence the value of call option with strike price 50 is lower than above price.