Question

The spot price per share is $115 and the risk free rate is 5% per annum on a continuously compounded basis. The annual volatility is 20% and the stock does not pay any dividend. All options have a one-year maturity. In answering the questions below use a binomial tree with three steps. Each step should be one-third of a year. Show your work.

1. Compute u, d, as well as p for the standard binomial model.

Answer 1

As per concept calculation in binomial model of option valuation :

pse"-d и –d .-р чл

the tree structure formed as

As strike price is not given, so assumed Strike price = spot price = 115.

The binomial model calculation based for Call Option, as

Strike price = 115
Discount factor per step = 0.9835
Time step, dt =1/3 = 0.3333 years, 121.67 days
Growth factor per step, a = 1.0168
Probability of up move, p = 0.5438
Up step size, U = 1.1224
Down step size, d = 0.8909

162.608 47.60798 144.87511 31.77592 129.0761 20.37097 129.0761 14.0761 115 12.70045 77527742 102.4589 102.4589 4.025752 91.28551 81.33057 Node Time: 0.0000 0.3333 0.6667 1.0000

Value of the Call option at t=0 , V =12.70045 ($ 12.70).