Question

A stock is expected to pay a dividend of $2.50 per share in two (2) months, in six(6) months and in eight(8) month. The stock price is $66, 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 nine-month forward contract on the stock.

1. What are the forward price and the initial value of the forward contract?

2. Five (5) months later, the price of the stock is $59 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?

Answer 1

Solution :-

(a) The forward price and the initial value of the forward contract :-

Present Value of Dividend = $2.50 * e ^{-0.08 *2/12} + $2.50 * e ^{-0.08 *6/12} + $2.50 * e ^{-0.08 *8/12}

=   ( $2.50 * 0.9867 ) + ( $2.50 * 0.96079 ) + ( $2.50 * e ^{-0.08 *8/12} + 0.94806 )

= $2.50 * 2.89555

= $7.24

Forward Price is therefore

F₀ = ( $66 - $7.24 ) * e ^{0.08 * 9/12}

F₀ = $58.76 * 1.0618 = $62.394

The Value at origination of a forward contract is ( $66 - $62.394 ) = $3.61

( b)

Present value of Dividend = $2.50 * e ^{-0.08 *2/12}

= ( $2.50 * 0.986755 )

= $2.467

Forward Price = ( $59 - $2.467 ) * e ^0.08*5/12

= $ 56.533 * 1.033895

= $58.449

Now the Value of short position = ( $62.394 - $58.449 ) * e^{-0.08 * 5/12}

= 3.9448 * 0.967216

= $ 3.8155

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