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.

- What are the forward price and the initial value of the forward contract?

- 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

F_{0} = ( $66 - $7.24 ) * e
^{0.08 * 9/12}

F_{0} = $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

If there is any doubt please ask in comments

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