- 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
Use the Black-Scholes-Merton model adjusted for cash flows on the underlying to calculate the price of a call option.
Exercise price: $100
Continuously compounded risk-free rate: 5.25%
Time to expiration: 2 years
Volatility: 0.3
Continuously compounded dividend yield: 2%
Underlying price: $125
Exercise price: $100
Continuously compounded risk-free rate: 5.25%
Time to expiration: 2 years
Volatility: 0.3
Continuously compounded dividend yield: 2%
Correct Answer: $36.38
d1 = {ln(120.1/100) + [0.0525 + (0.3)2/2] 2.0} / [0.3 (2.0)1/2] = 0.89132
d2 = 0.89132 - 0.3 (2.0)1/2 = 0.4671
N(d1) = N(0.89132) = 0.8133
N(d2) = N(0.4671) = 0.6808
c = 120.1 x 0.8133 - 100 e-0.0525 (2) x 0.6808 = 36.38
Adjust the price of the underlying to S0 = 125 e -0.02 (2.0) = 120.1.
d1 = {ln(120.1/100) + [0.0525 + (0.3)2/2] 2.0} / [0.3 (2.0)1/2] = 0.89132
d2 = 0.89132 - 0.3 (2.0)1/2 = 0.4671
N(d1) = N(0.89132) = 0.8133
N(d2) = N(0.4671) = 0.6808
c = 120.1 x 0.8133 - 100 e-0.0525 (2) x 0.6808 = 36.38
User Contributed Comments 4
| User | Comment |
|---|---|
| ssradja | how should i know n(d1) or d2. i thought they should give the table so we can find the right number. anybody? |
| Smiley225 | I cant see us being required to plug a bunch of figures BSM model in the exam.... |
| mcspaddj | What, we can't bring our laptops? |
| jperez049 | Should the carrying benefit of 2% compound dividend yield also be considered when calculating d1? I can see the adjusted price of the underlying but not in the calculation of d1... |