- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 38. Valuation of Contingent Claims
- Subject 2. Two-Period Binomial Model

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**CFA Practice Question**

A stock is worth $60 today. In a year the stock price can rise or fall by 15 percent. The interest rate is 6%. A put option expires in two years and has an exercise price of $60.

Use the two-period binomial model to calculate the put option price.

Correct Answer: $1.83

p

p

The risk-neutral probability is π = (1.06 - 0.85) / (1.15 - 0.85) = 0.7, and 1 - π = 0.3.

Stock prices in the binomial tree one and two years from now are:

- S
^{+}= 60 (1.15) = $69 - S
^{-}= 60 (0.85) = $51 - S
^{++}= 60 (1.15) (1.15) = $79.35 - S
^{+-}= S^{-+}= 60 (1.15) (0.85) = $58.65 - S
^{--}= 60 (0.85) (0.85) = $43.35

- p
^{++}= Max (0, 60 - 79.35) = $0 - p
^{+-}= p^{-+}= Max (0, 60 - 58.65) = $1.35 - p
^{--}= Max (0, 60 - 43.35) = $16.65

p

^{+}= (0.7 x 0 + 0.3 x 1.35)/(1.06) = $0.3821p

^{-}= (0.7 x 1.35 + 0.3 x 16.65)/(1.06) = $5.60The put price today is p = (0.7 x 0.3821 + 0.3 x 5.6)/1.06 = $1.83.

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**User Contributed Comments**
2

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

rhardin |
I guess we are to assume that this put is a European? |

Debashree |
@rhardin yes seems like that.. |