- 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 put expires in 150 days and has an exercise price of $100. The underlying stock is worth $105 and has a standard deviation of 0.2. The continuously compounded risk-free rate is 5.5%. Assume that the stock will pay a dividend of $3 on day 50. The price of the option should be ______.

A. $3.19

B. $7.44

C. $2.10

**Explanation:**The present value of the $3 dividend is: $3 e

^{-0.055 (50/365)}= $2.98.

Adjust the price of the underlying to S

_{0}= 105 - 2.98 = $102.02

d

_{1}= {ln(102.02 /100) + [0.055 + (0.2)

^{2}/2] (150/365)} / [0.2 (150/365)

^{1/2}] = 0.16

d

_{2}= 0.16 - 0.2 (150/365)

^{1/2}= 0.03

N(d

_{1}) = N(0.16) = 0.5636

N(d

_{2}) = N(0.03) = 0.5120

c = 102.02 x 0.5636 - 100

^{e-0.055 (150/365)}x 0.5120 = 7.44

p = 100 x e

^{-0.055 (150/365)}x [1 - 0.5120] - 102.02 x [1 - 0.5636] = 3.19

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**User Contributed Comments**
6

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

wink26 |
How do we calculate, or know, N(d1) and N(d2) without a table? |

humanitaire |
I don't think we are required to know that by the way... |

ptyson |
I gave up on this one as we didn't have the table! |

LloydBraun7 |
Don't get the D1 calculation...I get [0.0199 + (0.055 + 0.02)*0.411]/0.1282 = 0.3958. Any ideas where I went wrong? |

JohnnyWu |
Pretty frustrating without the table. |

kchoi |
I agree with the calculations by ptyson... |