Quantitative Finance:

Exercise 1 ( mark for each part). Consider a swap with fixed rate K starting at To and ending at T (a) Express the value of the swap VW(t) in terms of only zero coupon bond prices. (b) Assume t-T0-0, Tn-n and -1. Find numbers 1 and u (depending on n and K but not on any interest rates) such that SW (in other words, VR ) s bounded below by l and above by u). Justify your answer. Hint What is the smallest a ZCB price can be? What is the largest? (c) Consider a forward contract on a stock with price St at t. Let K be the delivery price and T be the maturity. Is the value of the forward contract VK (t, T) necessarily bounded above or below? Explain. You can assume for simplicity that the stock pays no income. Exercise 1 ( mark for each part). Consider a swap with fixed rate K starting at To and ending at T (a) Express the value of the swap VW(t) in terms of only zero coupon bond prices. (b) Assume t-T0-0, Tn-n and -1. Find numbers 1 and u (depending on n and K but not on any interest rates) such that SW (in other words, VR ) s bounded below by l and above by u). Justify your answer. Hint What is the smallest a ZCB price can be? What is the largest? (c) Consider a forward contract on a stock with price St at t. Let K be the delivery price and T be the maturity. Is the value of the forward contract VK (t, T) necessarily bounded above or below? Explain. You can assume for simplicity that the stock pays no income