FRM Part I · FRM Exam Part I · Exotic Options
A company will grant an at-the-money European call at the end of year 1, expiring at the end of year 3 (a forward start option). Volatility and interest rates are constant. Today, a 2-year at-the-money call on the stock, priced at 50, is worth 6.00. The stock now trades at 80. What is the value today of the forward start option?
The forward start option is worth 9.60. With constant volatility and rates, an at-the-money 2-year call is worth 12% of the stock price (6/50), so the forward start option today is 12% of 80.
- A9.60Correct
- B6.00
- C7.50
- D12.00
Explanation
Value scales with the stock price. The at-the-money 2-year call is worth 6/50 = 12% of the stock price. At the start date the option is at the money with 2 years left, so it will be worth 12% of S1. Today's value is therefore 0.12 x 80 = 9.60. Using 6.00 ignores the different stock price.
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