- CFA Exams
- CFA Level I Exam
- Topic 7. Derivatives
- Learning Module 32. Valuation of Contingent Claims
- Subject 4. Black-Scholes-Merton Option Valuation Model
CFA Practice Question
Consider a stock that trades for $75. A call 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 stock's return is 0.35, compute 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.
Correct Answer: $10.62
d2 = 0.5479 - 0.35 x (150/365)1/2 = 0.3235
N(d1) = N(0.55) = 0.7088
N(d2) = N(0.32) = 0.6255
c = $75 x 0.7088 - $70 x e -0.07 x (150/365) x 0.6255 = $10.62
d1 = {ln(75/70) + [0.07 + (0.352/2)] x (150/365)} / (0.35 (150/365)1/2) = 0.5479
d2 = 0.5479 - 0.35 x (150/365)1/2 = 0.3235
N(d1) = N(0.55) = 0.7088
N(d2) = N(0.32) = 0.6255
c = $75 x 0.7088 - $70 x e -0.07 x (150/365) x 0.6255 = $10.62
User Contributed Comments 6
| User | Comment |
|---|---|
| danlan2 | S=75 and X=70 |
| rhardin | The Schweser notes for 2010 say "it appears as though the candidate is no longer responsible for using the BSM model to actually price a call option." Is this true? I don't have the curriculum derivatives book with me, haha. |
| weiw | are we supposed to memorize the formula for bSM model? |
| Nando1 | Based on the LOS from reading 62, NO, we don't have to calculate an option price based on BSM. We do have to understand the BSM assumptions and how the input values impact the model. |
| ashish100 | Anyone calculated something else for d1 using that formula? |
| ashish100 | Nvm we good |