CFA Level I · CFA Level I Exam · Pricing and Valuation of Options
A non-dividend-paying stock trades at 52. A European call on it has an exercise price of 50, expires in one year, and the risk-free rate is 4% (annual compounding). The lower bound of the call price is closest to:
The lower bound is the stock price minus the present value of the exercise price: 52 minus 50/1.04, which is about 3.92. The exercise price must be discounted at the risk-free rate, so simply subtracting 50 to get 2.00 understates the bound.
- A2.00
- B3.92Correct
- C4.00
Explanation
Lower bound = max(0, S - X/(1+r)^T) = 52 - 50/1.04 = 52 - 48.08 = 3.92. Using 52 - 50 = 2.00 ignores discounting of the exercise price. 4.00 would come from compounding X upward (50 x 1.04 = 52, then... a wrong adjustment) and is not the bound.
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