Derivative Paper

Problem 5.29.

A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.

a)     What are the forward price and the initial value of the forward contract?

b)   Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?

A. First we need to find the Initial value of the dividends that occur in 2 months and 5 months….The equation to find this value is: I = e^-rt. So given this equation, the value of the dividends at 2 and 5 months is: I = 1(e^-0.08x0.1666) + 1(e^-0.08x0.41666) = 1.95. We then add this value to the Forward price equation of Fo = (So – I)e^rt. The result from this equation is: Fo = (50 – 1.95)e^0.08x0.5 = 50.01

B. B) First we need to find the initial value of the first dividend (2 month). The 5th month dividend isn’t included because we haven’t reached that point in time yet. The process is the same as above. I = e^-rt. The result is: I = e^-0.08x0.1666 = 0.9868. We add this to our equation to find the value of our short position and forward contract price. The short position value is found by the equation f = -(S – I – Ke^-rt). This produces a result of f = -(48 – 0.9868 – 50.01e^-0.08x0.25) = 2.01. We then find the forward price by equation (So – I)e^rt. Therefore the forward price is Fo = (48 – 0.9868)e^0.08x0.25 = 47.96