Consider a one period (t 0 and t 1) binomial world in which the current stock price of 100 can either go up by 25 percent or down by 20 percent Assume the probabilities of the uptick and the downtick are 70 and 30 , respectively The risk free rate is 7 percent, and the expected return on the market portfolio is 12 Both call and put options with an exercise price of 100 are available in the market Questions What would be the call's price if the stock goes up at t 1 $20 B $25 C $30 D $40 What would be the call's price if the stock goes down at t 1 $ 20 B $0 C $5 D $10 What is the hedge ratio of the call option at t 0 0 333 B 0 4333 C 0 55556 D 0 75 What is the theoretical value of the call option at t 0 $14 02 B 15 67 C 16 12 D $17 53 What is the hedge ratio of the put option at t 0 0 75 B 0 6667 C 0 5556 D 0 4444 E 0 25 What is the theoretical value of the put option at t 0 6 25 B 7 48 C 7 67 D 8 05 E 8 60 What is the expected return on the stock 11 5 B 14 C 14 5 D 15 E 16 5 What is the expected return on the call option 24 83 B 28 43 C 34 33 D 38 67 E 42 16 What is the beta of the stock based on the CAPM 0 75 B 0 9 C 1 2 D 1 4 E 1 6 What is the beta of the call option based on the CAPM 3 33 B 3 57 C 5 68 D 6 34 E 7 12 What is the omega (elasticity) of the call option 2 73 B 3 23 C 3 96 D 4 16 E 4 89 Now extend the one period binomial model to a two period world (t 0, t 1, t 2) for the next 5 questions Question What is the value of the call if the stock goes up, then down $0 B $4 C $14 D $30 E $69 What is the hedge ratio at t 1 if the stock goes up one period 0 9 B 0 925 C 0 95 D 1 0 E 1 1 What is the theoretical value of the call option at t 1 if the stock goes up one period $23 23 B $25 31 C $29 38 D $31 54 E $36 54 What is the theoretical value of the call option at t 0 $17 69 B $18 87 C $19 31 D $20 74 E $25 41 What is the hedge ratio at t 0 0 65 B 0 7 C 0 76 D 0 85 E 1 0

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Consider a one-period (t=0 and t=1) binomial world in which the current stock price of 100 can either go up by 25 percent or down by 20 percent.

Assume the probabilities of the uptick and the downtick are 70% and 30%, respectively.

The risk-free rate is 7 percent, and the expected return on the market portfolio is 12%.

Both call and put options with an exercise price of 100 are available in the market.

Questions: What would be the call's price if the stock goes up at t=1?
1. $20 B. $25 C. $30 D. $40
What would be the call's price if the stock goes down at t=1?
1. $-20 B. $0 C. $5 D. $10
What is the hedge ratio of the call option at t=0?
1. 0.333 B. 0.4333 C. 0.55556 D. 0.75
What is the theoretical value of the call option at t=0?
1. $14.02 B. 15.67. C. 16.12 D. $17.53
What is the hedge ratio of the put option at t=0?
1. -0.75 B. -0.6667 C. -0.5556. D. -0.4444 E. -0.25
What is the theoretical value of the put option at t=0?
1. 6.25 B. 7.48 C. 7.67 D. 8.05 E. 8.60
What is the expected return on the stock?
1. 11.5% B. 14% C. 14.5% D. 15% E. 16.5%
What is the expected return on the call option?
1. 24.83% B. 28.43% C. 34.33% D. 38.67% E. 42.16%
What is the beta of the stock based on the CAPM?
1. 0.75 B. 0.9 C. 1.2 D. 1.4 E. 1.6
What is the beta of the call option based on the CAPM?
1. 3.33 B. 3.57 C. 5.68 D. 6.34 E. 7.12
What is the omega (elasticity) of the call option?
1. 2.73 B. 3.23 C. 3.96 D. 4.16 E. 4.89

Now extend the one-period binomial model to a two-period world (t=0, t=1, t=2) for the next 5 questions.

Question: What is the value of the call if the stock goes up, then down?
1. $0 B. $4 C. $14 D. $30 E. $69
What is the hedge ratio at t=1 if the stock goes up one period?
1. 0.9 B. 0.925 C. 0.95 D. 1.0 E. 1.1
What is the theoretical value of the call option at t=1 if the stock goes up one period?
1. $23.23 B. $25.31 C. $29.38 D. $31.54 E. $36.54
What is the theoretical value of the call option at t=0?
1. $17.69 B. $18.87 C. $19.31 D. $20.74 E. $25.41
What is the hedge ratio at t=0?
1. 0.65 B. 0.7 C. 0.76 D. 0.85 E. 1.0