- CFA Exams
- CFA Exam: Level I 2021
- Study Session 16. Derivatives
- Reading 49. Basics of Derivative Pricing and Valuation
- Subject 11. Binomial Valuation of Options

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**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

S

p

p

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 = $66S

^{-}= 55 x 0.84 = 46.2p

^{+}= Max (0, $60 - $66) = $0p

^{-}= Max (0, $60 - $46.2) = $13.8p = (0.5833 x 0 + 0.4167 x 13.8) / 1.05 = $5.48

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**User Contributed Comments**
3

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. |