FRM Part I · FRM Exam Part I · Properties of Options
A European put has strike USD 60 and six months to expiry on a stock priced at USD 55 that pays no dividends. The risk-free rate is 4% continuously compounded. What is the lower bound on the put price (to the nearest cent)?
The lower bound is USD 3.81. For a European put on a non-dividend stock it is the present value of the strike minus the stock price: 60 times e^-0.02 is 58.81, less 55 gives 3.81. Using undiscounted intrinsic value of USD 5.00 is incorrect for European puts.
- AUSD 5.00
- BUSD 3.81
- CUSD 4.00
- DUSD 5.81Correct
Explanation
Lower bound = K e^(-rT) - S0 = 60 e^(-0.02) - 55 = 60(0.980199) - 55 = 58.81 - 55 = 3.81. Check: 58.812 - 55 = 3.812. Option USD 5.81 is wrong; USD 5.00 is the undiscounted intrinsic value, which is not the European bound.
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