Question

The volatility of a stock is 0.3 per annum. In a Cox-Ross-Rubinstein binomial tree in which one step represents a time interval of 3 months, what are the proportional up-movement and down-movement factors, u and d, respectively?

a. u=1.16, d=0.86

b. u=1.30, d=0.70

c. u=1.24, d=0.81

d. u=1.35, d=0.74

Answer 1

u=e^(volatility*sqrt(t))=e^(0.3*sqrt(3/12))=1.161834243

d=e^(-volatility*sqrt(t))=e^(-0.3*sqrt(3/12))=0.860707976