Chapter 9 Forward Price Proof b)

[Avviey]

I have another question re the forward price proof b) on page 16 of chapter 9.

It says at time 0, thee are portfolios:

A: one long forward contract
B: borrow Ke^(-rT) cash and buy one share at S0.

If we hold both of these portfolios up to time T, then both have a value of ST-K at time T.

I understand portfolio B has value of B is Ke^(-rT) ,but I dont understand why portfolio has the same value. One long forward contract means buying the underlying one share of the forward contract?

Thank you very much if someone can help.

 

[didster]

A: Agree to buy underling at price K, so at expiry you buy at K and can sell at S_T, so the contract has net value of S_T - K.

B: at time T, you need to pay back K, ie Ke^(-rT) with interest at risk free rate;
and can sell your stock for S_T so net value is again S_T-K

Whether you need to hold the stock after expiry is irrelavant to pricing(theoretically), but net positions at expiry need to be the same for comparison, in this case holding (oweing) net value of contract and not holding stock.

 

[Avviey]

hi didster,

ok, its a forward, therefore regardless of the price of the share, holder has to buy the share at K, hence the value of a is ST-K, which can be positive or negative. got you. thanks very much.