FRM Part I · FRM Exam Part I · Properties of Options
Two American call options on the same non-dividend-paying stock have the same strike but different maturities, 3 months and 9 months. Which statement is correct?
The 9-month American call must be worth at least as much as the 3-month call. The longer option can be exercised at any time the shorter one can, and also later, so it offers at least the same rights and cannot be cheaper.
- AThe 3-month call must be worth more than the 9-month call
- BThe 9-month call must be worth at least as much as the 3-month callCorrect
- CThe two must have identical values
- DThe 9-month call is worth less because of discounting of the strike
Explanation
An American option with longer maturity includes all exercise opportunities of the shorter one plus more, so it cannot be worth less. Discounting does not reverse this for American options.
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