# Let S(t) be the time-t price of a nondividend-paying stock. For a three-period binomial stock price model,

## Question:

Let S(t) be the time-t price of a nondividend-paying stock. For a three-period binomial stock price model, you are given:

(i) The length of each period is one year.

(ii) S(0) = 100.

(iii) u = 1.1, where u is one plus the percentage change in the stock price per period if the price goes up.

(iv) d = 1/1.1, where d is one plus the percentage change in the stock price per period if the price goes down.

(v) The continuously compounded risk-free interest rate is 5%.

Consider a special derivative which pays, at the end of three years,

Calculate the current price of this derivative.

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