- 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**

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

d

d

N(d

N(d

c = 120.1 x 0.8133 - 100

Adjust the price of the underlying to S

_{0}= 125^{e -0.02 (2.0)}= 120.1.d

_{1}= {ln(120.1/100) + [0.0525 + (0.3)^{2}/2] 2.0} / [0.3 (2.0)^{1/2}] = 0.89132d

_{2}= 0.89132 - 0.3 (2.0)^{1/2}= 0.4671N(d

_{1}) = N(0.89132) = 0.8133N(d

_{2}) = N(0.4671) = 0.6808c = 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... |