- 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. If the interest rate is 6%, what is the price of a call option that expires in two years and has an exercise price of $55?

A. $17.11

B. $11.98

C. $2.41

**Explanation:**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

- c
^{++}= Max (0, 79.35 - 55) = $24.35 - c
^{+-}= c-+ = Max (0, 58.65 - 55) = $3.65 - c
^{--}= Max (0, $43.35 - 55) = $0

^{+}= (0.7 x 24.35 + 0.3 x 3.65)/(1.06) = $17.11.

c

^{-}= (0.7 x 3.65 + 0.3 x 0)/(1.06) = $2.41

The call price today is c = (0.7 x 17.11 + 0.3 x 2.41)/1.06 = $11.98.

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**User Contributed Comments**
4

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

janis36 |
Shortcuts? Anyone? |

bruno5104 |
Probably not... |

happey |
Guessing... 2.4$ seems too low for a two year option, 17$ way too high -> therefore Answer B (but this requires some experience with options) |

syvestro |
Not really, but generally speaking this type of crunchy problem is one you'll want to try to calculate out if you have any time at all to do so. The other thing to look at is that you can quickly have a pi ratio of 0.7, which means that 24 * 0.7 = 16.8.....so 17 is too high even if you assume there's zero discounting and don't factor in other outcomes. |