- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 38. Valuation of Contingent Claims
- Subject 4. Black-Scholes-Merton Option Valuation Model

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**CFA Practice Question**

A stock sells for $110. A call option on the stock has an exercise price of $105 and expires in 43 days. If the continuously compounding interest rate is 0.11 and the standard deviation of the stock's returns is 0.25, what is the price of the call option according to the Black-Scholes-Merton model?

Below is the relevant part of the cumulative probabilities table for a standard normal distribution.

A. 6.95

B. 7.82

C. 8.08

**Explanation:**d

_{1}= {ln(110/105) + [0.11 + (0.25

^{2}/2)] x (43/365)} / (0.25 (43/365)

^{1/2}) = 0.7361

d

_{2}= 0.7361 - 0.25 x (43/365)

^{1/2}= 0.6503

N(d

_{1}) = N(0.74) = 0.7704

N(d

_{2}) = N(0.65) = 0.7422

c = $110 x 0.7704 - $105 x e

^{-0.11 x (43/365)}x 0.7422 = $7.82

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**User Contributed Comments**
5

User |
Comment |
---|---|

aero |
This question is very time consume... I don't think that you are going to have enough time during the test..... |

tengo |
medium tehnical difficulty but difficult and tedious in terms of time and stress |

americade |
too much for day of test, i don't think BS will be tested where formula has to be known and figured. i guess it is a possibility to get a question given the d1 and d2 values to calc the call/put. Unlikely to know any B/S other than general ques. |

nick1981 |
its more, the actual calculation of BS is not required, so guys don´t worry about those questions, just get the overall concept right for the famous statement right or wrong questions. |

janis36 |
are there any shortcuts to getting this question right? |