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. Please explain each step in your computations. Construct a confidence interval for the price, explaining each step. Attach the output of your excel computations which illustrate exactly what you have done.

Answer 1

1. modeling the stock price
2. determining the rate of return
3. we calculate the dividends from the forecasted exchange rate received
4. we calculate the dividends from the received forecasted exchange rate and determine the fair price