FRM Part I · FRM Exam Part I · Options Markets
A non-dividend-paying stock trades at USD 50. A European call with strike USD 45 expires in one year, and the continuously compounded risk-free rate is 4%. What is the lower bound for the call price (nearest cent)?
The lower bound is the stock price minus the present value of the strike: 50 minus 45 discounted at 4% for one year, which is 50 − 43.24 = USD 6.76. Using the undiscounted strike gives USD 5.00, which understates the bound.
- AUSD 5.00
- BUSD 6.76Correct
- CUSD 3.24
- DUSD 6.00
Explanation
Lower bound = max(S - K e^{-rT}, 0). Here 45 × e^{-0.04} = 45 × 0.960789 = 43.236. So the bound is 50 - 43.24 = 6.76. USD 5.00 ignores discounting of the strike, which is the key mistake.
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