- 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**

Consider a stock that trades for $75. A put on this stock has an exercise price of $70 and it expires in 150 days. If the continuously compounding interest rate is 7% and the standard deviation for the stocks return is 0.35, compute the price of the put option according to Black-Scholes-Merton model.

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

Correct Answer: $3.63

d

N(d

N(d

p = $70 x e

d

_{1}= {ln(75/70) + [0.07 + (0.35^{2}/2)] x (150/365)} / (0.35 (150/365)^{1/2}) = 0.5479d

_{2}= 0.5479 - 0.35 x (150/365)^{1/2}= 0.3235N(d

_{1}) = N(0.55) = 0.7088N(d

_{2}) = N(0.32) = 0.6255p = $70 x e

^{-0.07 x (150/365)}x (1 - 0.6255) - $75 x (1 - 0.7088) = $3.63###
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