1. Futures versus Forwards. Let to 0,61,t2, ... denote dates where tn is n days from today (to). An asset's price is $1,000 today, Ato) = 1000, and the continuously compounded interest rates is constant, r = 4% with fractions of time calculated Act/365: ti+1-ti = 1/365. (a) What is the 10-day forward price of the asset, FA(0,610)? (b) You agree today (to = 0) to buy the asset in 10 days for K = FA(0,t10). How much do you need to pay /receive today to enter into this contract? (c) Assume the asset's price increases by $10 each day for the next 10 days, A(tn) = A(0) + 10n, and compute the missing entries in the following table where CFFut is the cash flow for 1 futures contract, CFFud is the cash flow for 1 forward contract, QFut is the number of futures contracts needed to replicate 1 forward contract, and FVQxCF) is the corresponding cash flow of the modified futures contract, future valued to tlo. n A(tn) Fatn,t10) VFA(tr, 10, K) CFFwd CFFut Fut 1,000 0 1,010 FVQxCF)Fut 0 0 1 10 1,100 1,100 X (d) Compare the total cash flows of 1 (unmodified) futures contract versus the forward contract. (e) Would Q Fut's be different if the underlying had instead dropped by $10 each day to settle at $900 at t10? 1. Futures versus Forwards. Let to 0,61,t2, ... denote dates where tn is n days from today (to). An asset's price is $1,000 today, Ato) = 1000, and the continuously compounded interest rates is constant, r = 4% with fractions of time calculated Act/365: ti+1-ti = 1/365. (a) What is the 10-day forward price of the asset, FA(0,610)? (b) You agree today (to = 0) to buy the asset in 10 days for K = FA(0,t10). How much do you need to pay /receive today to enter into this contract? (c) Assume the asset's price increases by $10 each day for the next 10 days, A(tn) = A(0) + 10n, and compute the missing entries in the following table where CFFut is the cash flow for 1 futures contract, CFFud is the cash flow for 1 forward contract, QFut is the number of futures contracts needed to replicate 1 forward contract, and FVQxCF) is the corresponding cash flow of the modified futures contract, future valued to tlo. n A(tn) Fatn,t10) VFA(tr, 10, K) CFFwd CFFut Fut 1,000 0 1,010 FVQxCF)Fut 0 0 1 10 1,100 1,100 X (d) Compare the total cash flows of 1 (unmodified) futures contract versus the forward contract. (e) Would Q Fut's be different if the underlying had instead dropped by $10 each day to settle at $900 at t10
