A forward contract on a stock is struck at time t so that no money is...

A forward contract on a stock is struck at time t so that no money is exchanged initially. The forward price is F, to be delivered at time T. However, there will be a dividend paid out by the stock at time td. What is known is that the dividend will be a known percentage, d, of the stock price. The dividend size, dS(td), depends on the unknown future stock price and so it is a random variable. Use a no arbitrage argument to determine the forward price F;

Expert Solution

F = forward price

T = Time to maturity

Td = Time at which the dividend will be paid

d= %dividend of the S(td) stock price

Lets assume, r = risk free rate & spot price of stock at present = S(t0)

Present Value of the dividend paid at time td:-

= dS(td)*e^(-r*td)

Forward price of the contract = F = (S(t0) - PV of Dividend)*e^(r*T)

= (S(t0) - dS(td)*e^(-r*td))*e^(r*T)

F = S(t0)*e^(r*T) - dS(td)*e^(td*T)

jeff jeffy answered 2 years ago

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