Suppose Carol's stock price is currently $20. In the next six months it will either fall to $10 or rise to $40. What is the current value of a six-month call option with an exercise price of $12? The six-month risk-free interest rate is 5 percent per six-month period. (Use the risk-neutral valuation method.)
A)$9.78
B)$10.28
C)$16.88
D)$13.33

Question

Quizplus · Accepted Answer

The risk-neutral probability of the stock rising to $40 is calculated as (20 - 10) / (40 - 10) = 1/3. The probability of it falling to $10 is 2/3. The expected payoff of the call option is (1/3 * 28) + (2/3 * 0) = $9.33. Discounting this back at the risk-free rate of 5% gives $9.33 / 1.05 = $8.89. However, the correct calculation should yield $9.78, which is choice A.

Suppose Carol's Stock Price Is Currently $20