Question

For a non-dividend paying stock with current stock price So, explain using the no -arbitrage argument why its forward price at time T from now should be Fo =So*e(T) ina world with no transaction cost, in which everyone can borrow or lend at the risk free rate r.

Answer 1

Forward Price at time T=F0

Let us assume, one makes a forward contract to sell one stock at price F0 at time T

He can borrow money at risk free interest rate and buy the stock at price S0 .

Now if ,as per forward contract he sells the share at time T, he will get F0.

As per no-arbitrage argument , the amount received by selling the share (F0) should be equal to the amount to be paid back with interest for the amount borrowed.

Future Value of amount borrowed at interest rate=r and time =T; S0*(e^(rT))

Hence,

F0=S0*(e^(rT))