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Question 6.6: Show that V (t) > [F(t,T) − F(0,T)]e^−r(T−t) leads to an ...

Show that  V (t) > [F(t, T) − F(0, T)]e^{−r(T−t)} leads to an arbitrage opportunity.

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At time t

  • borrow and pay (or receive and invest, if negative) the amount V (t) to acquire a short forward contract with forward price F(0, T) and delivery date T,
  • initiate a new long forward contact with forward price F(t, T) at no cost.
    Then at time T
  • close out both forward contracts receiving (or paying, if negative) the amounts S(T) − F(0, T) and S(T) − F(t, T), respectively;
  • collect V (t)e^{r(T−t)} from the risk-free investment, with interest.

The final balance V (t)e^{r(T−t)} − [F(t, T) − F(0, T)] > 0 will be your arbitrage profit.

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