Suppose you are given the following data:

(1) Risk-free yearly interest rate is r = 6%.

(2) The stock price follows:

S_t ? S_t?1 = ?S_t + ?S_t?_t

Where the ? is a serially uncorrelated binomial process assuming the following values:

The 0

(1) Volatility is 12% a year.

(2) The stock pays no dividends and the current stock price is 100.

Now consider the following questions.

(a) Suppose ? is equal to the risk-free interest rate:

? = r

And that the S_t is arbitrage-free. What is the value of p?

(b) Would a p = 1/3 be consistent with arbitrage-free S_t?

(c) Now suppose ? is given by:

? = r + risk premium

What do the p and ? represent under these conditions?

(d) Is it possible to determine the value of p?

Transcribed Image Text:

with probability P with probability 1- p +1 -1 II