Question

1) Suppose a security has a current price of $15.00, and Investor A expects the security price to increase by 10% in one year with 60% probability or decrease by 5% in one year with 40% probability. Investor B agrees with Investor A’s values of the future prices but feels that the likelihood of either future price occurring is 50%. Assuming a 3% annual risk-free rate, what is the price of a one-year call option that has a strike price of $15.00 (assuming the call can only be exercised at maturity) for each of these investors? Do the differing probabilities assigned by these investors affect the price of the call option?

Answer 1

For investor A

probability of increase in price by 10%: 60%

probability of decrease in price by 5%: 40%

Stock price if price goes up: $ 16.5

Stock price if price goes down: $ 14.25

Strike price of Call Option: $15

Option value at expiry if stock price goes up: $ 1.5

Option value at expiry if stock price goes down: $ 0

Expected value of Call Option at Expiry = 1.5x60% + 0x40% = $0.9

Therefore price of one-year call option = $0.9/(1+3%) = $ 0.87

For investor B

probability of increase in price by 10%: 50%

probability of decrease in price by 5%: 50%

Stock price if price goes up: $ 16.5

Stock price if price goes down: $ 14.25

Strike price of Call Option: $15

Option value at expiry if stock price goes up: $ 1.5

Option value at expiry if stock price goes down: $ 0

Expected value of Call Option at Expiry = 1.5x50% + 0x50% = $0.75

Therefore price of one-year call option = $0.75/(1+3%) = $ 0.73

Obviously, differing probabilities assigned by these investors affect the price of the call option. Because price of call option is primarily based on future expectation of stock price. And Future expections are measured using proabilities.

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