By considering one or more suitably chosen portfolios, which you should specify care- fully, and by applying the no-arbitrage principle, show that the value at time 120 of a forward contract struck at K> 0 and maturing at time T> t, on an underlying asset with spot price S,, t 0, paying dividends continuously at a rate q > 0, is f(t, S)= S, e-9 (T-1)-Ke-r(T-1) where r> 0 is the continuously-compounded constant risk-free rate of interest per annum. [4 marks] A company enters into a forward contract with a bank to sell a dividend-paying underly- ing asset for K at time T > 0. The spot price at time T turns out to be ST, > K. The company asks the bank if it can roll the contract forward until time T2, T2 > T, rather than settle at time T. The bank agrees to a new delivery price, K. Using the no-arbi- trage principle, derive an expression for K and explain how it should be calculated.