FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A European call on a non-dividend-paying stock has S0 = 50, K = 48, r = 5% continuously compounded, and T = 2 years (e^{-0.10} = 0.904837). The model gives N(d1) = 0.70 and N(d2) = 0.60. What is the BSM call value, to the nearest cent?
The call is worth about 8.94. Compute S0 N(d1) = 50 x 0.70 = 35.00, then subtract the discounted strike times N(d2): 48 x 0.904837 x 0.60 = 26.06. The result is 8.94. Skipping the discounting gives 6.20.
- A8.94Correct
- B6.20
- C2.37
- D7.60
Explanation
PV of strike = 48 x 0.904837 = 43.432. Call = 50 x 0.70 - 43.432 x 0.60 = 35.00 - 26.06 = 8.94. Not discounting the strike gives 35 - 28.8 = 6.20. 2.37 is the put value computed with N(-d). Discounting for one year only gives 7.60.
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