Question

I want to learn how to calculate the call-value/price for the binomial model tree, so that i can calculate the call and put option.

I just need to find out how to get the call value.

The current price of Natasha Corporation stock is $6. In each of the next two years, this stock

price can either go up by $2.50 or go down by $2. The stock pays no dividends. The one-year

risk-free interest rate is 2% and will remain constant. Using the Binomial Model

a) calculate the price of a two-year European call option on Natasha stock with a strike

price of $7.

b) calculate the price of a two-year European put option on Natasha stock with a strike

price of $7.

Answer 1

A binomial tree is a graphical representation of possible intrinsic values that an option may take at different nodes or time periods. The value of the option depends on the underlying stock or bond, and the value of the option at any node depends on the probability that the price of the underlying asset will either decrease or increase at any given node.

Example:

There are a few major assumptions in a binomial option pricing model: 1) only two possible prices, one up and one down; 2) the underlying asset pays no dividends; 3) interest rate is constant; and, 4) no taxes and transaction costs.

Assume a stock price of $100, option strike price of $100, one-year expiration date, and interest rate (r) of 5%. At the end of the year there is a 50% probability the stock will rise to $125 and 50% probability it will drop to to $90. If the stock rises to $125 the value of the option will be $25 ($125 stock price minus $100 strike price) and if it drops to $90 the option will be worthless. The option value will be:

Option value = [(probability of rise*up value) + (probability of drop*down value)] / (1+r) = [(0.50*$25) + (0.50*$0)] / (1+0.05) = $11.90

Part 2 (a)

Formula - S= 6 , K= 7, Cu=6+2.5= 8.5-7=1.5 , Cd= 6-2= 4-7<6=0 , u = Cu/S 8.5/6= 1.42, d= 4/6= 0.67

P= (R-d)/(u-d) = P ((1+2%)^2-0.67)/(1.42-.67)= 0.5

Option value of Call= (P*Cu+(1-p)Cd)/(1+r)^t = 0.5*1.5+0.5*0)/(1+0.02)^2= 0.72

Option value of Put = )