15. Using the assumptions below, calculate the value of a European?style put option using a one?period binomial model:

Stock price: USD 50

Strike price: USD 45

Annual risk?free rate = 5.5%

Annual volatility: 36%

Dividend yield = 0%

Time to expiration = 1 year

A. 4.90

B. 5.18

C. 5.00

D. 4.67

Correct answer is Afficeffice" />

A is correct: these are the calculation: u=exp(0.36)= 1.4333 d=1/u= 0.6977. Then we have to calculate pup=[exp(0.55)?0.6977]/(1.4333?0.6977)= 0.4878, so pdown=1?0.4878= 0.5122.

S0up= S0*u=71.6665    S0down=S0*d=34.8838

 The value of the put option in one stage procedure is= exp(?0.055)*[0.4878*max(45?34.8838;0)+(1?0.4878)*max(45?71.6665;0)] = 4.9042$

B is incorrect: it results from the right calculation with the exemption of the last passage that lacks the discounting factor: [0.4878*max(45?34.8838;0)+(1?0.4878)*max(45?71.6665;0)]= 5.1815$

C is incorrect it is simply the intrinsic value of the corresponding call option: (50?45)$.= 5$

D is incorrect: it results from a right calculation with the exemption of the last passage in which there is a wrong inversion of the probabilties: exp(?0.055)*[(1?0.4878)*max(45?34.8838;0)+       0.4878*max(45?71.6665;0)]= 4.6706$

Reference: John Hull, Option, Futures and Other Derivatives, 5th ed. (ffice:smarttags" />New York: Prentice Hall, 2002), Chapter 8, Chapter 10.

Type of question: Market Risk