Question

Exhibit 1. Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent and the call exercise price 80.
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6. Consider the information given in Exhibit 1. Assume the one-period binomial model. What is the hedge ratio?

7. Consider the information given in Exhibit 1. Assume the one-period binomial model. What is the theoretical value of the call?

8. Consider the information given in Exhibit 1. Assume the two-period binomial model. What is the hedge ratio if the stock goes down one period?

9. Consider the information given in Exhibit 1. Assume the two-period binomial model. What is the current value of the call?

Answer 1

Stock can go up by 10%

U= upmove factor = 1+.01=1.1

Stock can go down by 8%

D= downmove factor= 1-0.08=0.92

C+= value of call option if it goes up=8

C-= value of call option if it goes down=0

Formula 1:H={(c+)-(c-)}/{(s+)-(s-)}

Answer 6 putting values= 8/14.4= hedge ratio = 0.55

Answer 7 The value of call= [(c+)*probability of upmove]+ [(c-)* probability of downmove]/(1+risk free rate)= 8*0.667/1.04= 5.131

Answer 8 using formula 1= [(c+-)-(c--)]/[(s+-)-(s--)]

(0.96-0)/(80.96-67.712)= 0.072

Answer9 see pic

Call value in 2 period binomial =11.41