- CFA Exams
- CFA Level I Exam
- Topic 7. Derivatives
- Learning Module 34. Valuation of Contingent Claims
- Subject 5. Black Option Valuation Model
CFA Practice Question
A forward contract is priced at $129. A European option on the forward contract has an exercise price of $135 and expires in 49 days. The continuously compounded risk-free rate is 3.75% and volatility is 0.25. Calculate the prices of a call option and a put option on the forward contract.
Correct Answer: 2.3229 and 8.2927
d1 = [ln(129/135) + (0.25)2/2 x 0.1342] / (0.25 x 0.13421/2) = -0.4505
d2 = -0.4505 - 0.25 x 0.13421/2 = -0.5421
N(d1) = N(-0.4505) = 1 - N(0.4505) = 1 - 0.6736 = 0.3264
N(d2) = N(-0.5421) = 1 - N(0.5421) = 1 - 0.7054 = 0.2946
p = e-0.0375 x 0.1342 [135 x (1 - 0.2946) - 129 x (1 - 0.3264)] = 8.2927
First calculate T: T = 49/365 = 0.1342.
Then calculate the values of d1 and d2.
d1 = [ln(129/135) + (0.25)2/2 x 0.1342] / (0.25 x 0.13421/2) = -0.4505
d2 = -0.4505 - 0.25 x 0.13421/2 = -0.5421
Using the normal distribution table,
N(d1) = N(-0.4505) = 1 - N(0.4505) = 1 - 0.6736 = 0.3264
N(d2) = N(-0.5421) = 1 - N(0.5421) = 1 - 0.7054 = 0.2946
c = e-0.0375 x 0.1342 (129 x 0.3264 - 135 x 0.2946) = 2.3229
p = e-0.0375 x 0.1342 [135 x (1 - 0.2946) - 129 x (1 - 0.3264)] = 8.2927
User Contributed Comments 4
| User | Comment |
|---|---|
| danlan2 | 129 is the future price. |
| NIKKIZ | It seems to me that there's a bit missing from the calculation of N(d1). I think it should be: {ln(129/135)+[0.0375+(0.25^2/2)]0.13425}/[0.25 X 0.13425^0.5]. The answer would be -0.39553. Am I missing something? |
| Greatrussian | NIKKIZ: The risk free rate 0.0375 should not be used in the calculation of d1. |
| maxsouto | NIKKIZ: The value of an option can't be less than 0 |