- 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 call option expires in two years and has an exercise price of $55. Today at time 0, a risk-free hedge consists of a short position in 10,000 calls and a long position in ______ shares of the stock.

A. 5865

B. 7935

C. 8167

**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

At the current price of $60, n = (c

^{+}- c

^{-}) / (S

^{+}- S

^{-}) = (17.11 - 2.41) / (69 - 51) = 0.8167.

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**User Contributed Comments**
5

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

HenryQ |
Don't understand why d=0.85 instead of 1/1.15= 0.87...anyone? |

heinzlive |
It is always u= 1+ upside potential in % and d= 1- downside potential in % thus, here u=1+0,15 = 1,15 and d= 1-0,15 = 0,85. |

dblueroom |
somehow you can't use 1/1.15 (schweser uses this) however, here as well as CFA book only recognize an downside move 1-.15 in this case. |

serboc |
I agree with DBlueroom |

dakota6789 |
the reason I think you can't use 1/15 is that a 15% increase on a 15% decrease is not the same thing. If I lose 15% of 100, I'm left with 85. If I gain 15% of 85, that's less than 100. |