The spot price of a stock index that follows a geometric Brownian motion is currently 4000 and over the next year it will pay dividends at a continuous rate of (delta =) 3% against a continuous risk-free rate of (r =) 3%. Its annual standard deviation is (sigma =) 20% p.a continuous.

REQUIRED

1.What is the forward price at which you could trade the index now for delivery in a year?

2.For real world expectations, you should use a prospective return of (mu =) 7% continuous including dividends and a dividend yield of 3%.

What price level must the index attain in a year to reach its prospective return

3.For a one year call option with a strike (X) the same as the forward price you calculated above, say in words only how to evaluate the risk neutral probability that the index exceeds this forward price (mention the Excel function you would use)?