A stock follows a Geometric Brownian Motion. This means its log returns are normal and the stock

Fantastic news! We've Found the answer you've been seeking!

Question:

A stock follows a Geometric Brownian Motion. This means its log returns are normal and the stock price will be lognormal. The annualized expected value of the log returns is 20%, and the annualized the standard deviation is 30%. The risk free rate is 5% continuously compounded and the dividend yield is 2% also continuously compounded. The initial stock price is $30.

An investor buys a weird product. It pays out the stock price in odd years and the stock price/2 in even years. This continues for 6 years. There is no cash flow in year zero, so this product produces 6 cash flows in years 1,2,3,4,5,6. On top of this in year 6 the contract pays out max(2*S(6)-60,0)

What is the fair price of this weird contract. Explain each step in your computations. Construct a confidence interval for the price, explaining each step.