Question

On June 15, you took a long forward contract (delivery on December 15) on a dividend-paying stock when the stock price was $30 and the risk-free interest rate (with discrete compounding) is 12% per annum. The amount of the dividends were known as $0.75 on Aug 15, and Nov 15. It is now September 15 and the current stock price and the risk-free interest rate are, respectively, $31 and 10%. What is the value of your long forward position now? Assume the forward contract prices are arbitrage free prices.

Answer 1

The price of a forward contract is calculated by subtracting the Present Value (PV) of dividends from the spot price as in case of forward contracts dividends are not received by the holder of forward position.

Forward price at the initiation of the contract-

The same can be calculated as

F=S-D*(1/1+Rf)^t/T

=$30-{[0.75*(1/1.12)^(2/12)]+[0.75*(1/1.12)^(5/12)]}

=$30-$0.735-$0.715

=$28.55

where,

F = Forward price

S= Spot price

D= Dividend to be received

Rf= Current Risk free rate

Calculation of value of forward position on September 15

At this point the first dividend is not relevant 2nd dividend is.

F=S-D*(1/1+Rf)^t/T

=$31-{[0.75*(1/1.10)^(2/12)]

=$31-0.738

=30.262

The value of contract is-

V(0,T)= F(3,12)-F(6,12)/(1.10)^3/12

= 30.262-(28.55/1.1^3/12)

=30.262-27.877

=$2.385

Value of contract = $2.385