FRM Part I · FRM Exam Part I · Properties of Options
A European put has strike 40 and expires in two years. The continuously compounded risk-free rate is 6% per year. What is the highest price the European put can have without creating an arbitrage opportunity?
The upper bound for a European put is the present value of the strike, 40e^(-0.12), which is about 35.48. The put can pay at most the strike at expiry. The figure 40.00 applies to American puts, which can be exercised immediately.
- A35.48Correct
- B40.00
- C4.52
- D37.67
Explanation
The payoff of a European put can never exceed K at expiry, so its price cannot exceed the present value of K: 40 x e^(-0.06 x 2) = 40 x 0.88692 = 35.48. The value 40.00 is the upper bound for an American put, which can be exercised immediately. The value 37.67 discounts for only one year. The value 4.52 is the difference 40 - 35.48, not a bound.
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