1 Binomial Tree Pricing Method

Two-periods Model (Today -> Six month -> One year)

Let us consider a two periods (or six-months per period) binomial tree option pricing model. Assume that in

the first period, the asset price can increase from $20 to $25 or fall from $20 to $17. In the second period if the

price increased to $25, the price could increase again to $30 or decrease to $24; or, if in the first period it

decreased to $17, in the second period in can either increase up to $24 or decrease again and fall to $14.

Let us assume riskless interest rate per period (or per six-month) is 2%.

(1) What is the price today of a one-year call option with a strike price of $22?

Hint: Work backwards, one year -> six month -> today. You need to solve for three nodes