Question #42
Reading: Reading 31 Valuation of Contingent Claims
PDF File: Reading 31 Valuation of Contingent Claims.pdf
Page: 18
Status: Unattempted
Question
A stock is priced at 40 and the periodic risk-free rate of interest is 8%. The value of a two- period European call option with a strike price of 37 on a share of stock using a binomial model with an up factor of 1.20 and down factor of 0.833 is closest to:
Answer Choices:
A. $9.13
B. $9.25
C. $3.57
Explanation
First, calculate the probability of an up move or a down move:
Pu = (1 + 0.08 − 0.833) / (1.20 − 0.833) = 0.673
Pd = 1 − 0.673 = 0.327
Two up moves produce a stock price of 40 × 1.44 = 57.60 and a call value at the end of two
periods of 20.60. An up and a down move leave the stock price unchanged at 40 and
produce a call value of 3. Two down moves result in the option being out of the money.
The value of the call option is discounted back one year and then discounted back again to
today. The calculations are as follows:
C+ = [20.6(0.673) + 3(0.327)] / 1.08 = 13.745
C- = [3(0.673) + 0 (0.327)] / 1.08 = 1.869
Call value today = [13.745(0.673) + 1.869(0.327)] / 1.08 = 9.13