- CFA Exams
- CFA Level I Exam
- Topic 7. Derivatives
- Learning Module 10. Valuing a Derivative Using a One-Period Binomial Model
- Subject 1. Binomial Valuation of Options
CFA Practice Question
Continue with question 1. Assume a stock price is $55 and that in the next year it will either rise by 20% or fall by 16%. The risk-free interest rate is 5%. A put option on this stock has an exercise price of $60. Determine its price.
Correct Answer: $5.48
π = (1.05 - 0.84) / (1.2 - 0.84) = 0.5833
S+ = 55 x 1.2 = $66
S- = 55 x 0.84 = 46.2
p+ = Max (0, $60 - $66) = $0
p- = Max (0, $60 - $46.2) = $13.8
p = (0.5833 x 0 + 0.4167 x 13.8) / 1.05 = $5.48
μ = 1.2 and d = 0.84
π = (1.05 - 0.84) / (1.2 - 0.84) = 0.5833
S+ = 55 x 1.2 = $66
S- = 55 x 0.84 = 46.2
p+ = Max (0, $60 - $66) = $0
p- = Max (0, $60 - $46.2) = $13.8
p = (0.5833 x 0 + 0.4167 x 13.8) / 1.05 = $5.48
User Contributed Comments 4
| User | Comment |
|---|---|
| yly14 | calculation for pi is the same for put or call. "d" accounts for the decrease in stock price, not the amount in-the-money of call or put. |
| AusPhD | 3.33 + 60/1.05 - 55 = Put price |
| jd2442424 | Can also use: n = (p_ - p+) / (S+ - S_) PV(TV) = (n * s+ - p+ * 0) / (1 + r)^t p0 = PV(TV) - so * n This would be easier if the 62.3 used n correctly. |
| RAMOST | Put call parity is the fastest way |