CFA Level I · CFA Level I Exam · Pricing and Valuation of Options
A non-dividend-paying stock trades at 50. A European call has an exercise price of 50 and six months to expiration, and the continuously compounded risk-free rate is 4%. In the BSM model, N(d1) = 0.60 and N(d2) = 0.55. The call value is closest to:
The call value is about 3.04. It equals the stock price times N(d1), which is 30, minus the present value of the exercise price (50 × e^(−0.02) = 49.01) times N(d2), which is 26.96. Failing to discount the strike gives 2.50.
- A0.59
- B2.50
- C3.04Correct
Explanation
Call = S×N(d1) − X×e^(−rT)×N(d2). e^(−0.02) = 0.980199. Call = 50×0.60 − 50×0.980199×0.55 = 30 − 26.956 = 3.04. Omitting the discounting gives 2.50, which overstates the PV of the exercise price and understates the call.
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