Question

A company enters a forward contract with a bank to sell a stock for K1 at time T1. The spot price of the stock at time T1 proves to be S1(>K1). The company asks the bank if it can roll the contract forward until time T2(>T1) rather than settle at time T1. The bank agrees to do so, if the new contract with a new delivery price K2 has the same value as the original contract at time T1. The risk-free rate is r. What should be K2? [6 points]

Answer 1

Here, the bank has taken the long position as the companyhas taken a short position(by entering a forward contract to sell a stock ).

When the contract is rolled forward, until time T2. Now the contract has a delivery prce K2, the contract's value at time T1 is

V-new= S1 - (K2/(1+r)^(T2-T1))... this is the value at time T1

Now the original contract at time T1 would have expired

So Value at time T1 = S1-K1. as K1 is the delvery price as negotiated earlier

Equating the two Values

S1 - (K2/(1+r)^(T2-T1)) = S1-K1

So K1 = K2/((1+r)^(T2-T1))

K2= K1*(1+r)^(T2-T1)