- 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 put 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 put option according to the Black-Scholes-Merton model?

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

A. 1.46

B. 2.32

C. 2.78

**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

p = $105 x e

^{-0.11 x (43/365)}x (1 - 0.7422) - $110 x (1 - 0.7704) = $1.46

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**User Contributed Comments**
6

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

ThePessimist |
Note that we do NOT have to memorize the BSM formula, and thus don't have to be able to answer this question. We just have to be able to explain the BSM model's assumptions and limitations, and explain how its affected by each of the Greeks. |

solnce |
The BSM formula is not difficult at all. I like those questions. They are really easy. |

dblueroom |
At this stage of preparation, I dont think my brain has that room for BS model. I can still do a lot of practice questions, but am a bit weary of remembering anything new. don't know how you guys feel. |

ljamieson |
Nice job interview question... |

REITboy |
The Pessimist is right. No need for this question. Bonus points for solnce, though. Gold star for the day!!! |

sunday128 |
Thanks ThePessimist for the PSA |