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Consider a forward contract on a stock with spot price us $100 per share. the stock will pay a dividend of us $3 per share after 6 months. suppose that the risk-free rate is always 5% per annum with continuous compounding.

What is the 1-year forward price?

User KapsiR
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$100 stock pays out $3 dividend in 6 months. At 5% annual interest, that dividend is "worth" $2.82 now. Subtract that from the stock price to get the forward price: $100 - $2.82 = $97.18.

Here's how to calculate the 1-year forward price for the stock:

Present Value of Dividend: We need to determine the present value of the $3 dividend paid after 6 months. Using the continuous compounding formula for present value:

Present Value = Future Value / exp(Interest Rate * Time)

In this case:

  • Future Value = $3 dividend
  • Interest Rate = 5% per annum (0.05/2 for 6 months)
  • Time = 6 months (0.5 years)

Therefore, the present value of the dividend is:

Present Value = $3 / exp(0.05/2 * 0.5) ≈ $2.821

2. Forward Price: The forward price is calculated by subtracting the present value of the dividend from the spot price:

Forward Price = Spot Price - Present Value of Dividend

Plugging in the values:

Forward Price = $100 - $2.821 ≈ $97.18

Therefore, the 1-year forward price of the stock is approximately $97.18.

Remember, this is an approximation due to rounding in the present value calculation.

User Martin Ogden
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