FRM Part I · FRM Exam Part I · Properties of Options
A stock trades at USD 50. A European call with strike USD 48 and one year to expiry is on a non-dividend-paying stock. The risk-free rate is 5% continuously compounded. What is the lower bound for the call price (rounded to the nearest cent)?
The lower bound is USD 4.34. For a European call on a non-dividend stock it equals the stock price minus the present value of the strike: 50 minus 48 times e^-0.05, which is 50 minus 45.66. Ignoring discounting would give USD 2.00, which is wrong.
- AUSD 2.00
- BUSD 4.34Correct
- CUSD 0.00
- DUSD 6.34
Explanation
Lower bound = S0 - K e^(-rT) = 50 - 48 e^(-0.05) = 50 - 48(0.951229) = 50 - 45.66 = 4.34. USD 2.00 ignores discounting of the strike. USD 6.34 adds rather than subtracts the difference wrongly. Zero is a weaker bound.
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