Interest Rate Swap Let Ti, i-1, .n be a set of dates, on which payments of the f
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Interest Rate Swap Let Ti, i-1, .n be a set of dates, on which payments of the floating leg of an interest rate swap occur. The payoff of the floating leg of the swap at time Ti is Fi s where Fi is the reference rate of the floating leg and s is a constant spread. For simplicity, let's assume that the floating and fixed payments happen on the same dates. Also, r is the risk-free rate on the same tenor. Let N be the notional of the swap. 1 What is the fixed semiannual swap rate calculated from the risk-free rates? Please specify mathematical formula (no need for exact numerical result at this point) Let the semiannual swap rate calculated in 1) be the fixed leg payment of the swap. What is the constant spread s which sets the present value of the swap position to be zero? Please specify mathematical formula (no need for exact numerical result at this point) 2)Explanation / Answer
A wide variety of swaps are utilized in finance in order to hedge risks, including interest rate swap,asset swap, and currency swaps. An interest rate swap is a contractual agreement between two parties agreeing to exchange cash flows of an underlying asset for a fixed period of time. The two parties are often referred to as counterparties and typically represent financial institutions. Vanilla swaps are the most common type of interest rate swaps. These convert floating interest payments into fixed interest payments and vice versa.
How Is the Fixed Rate Determined?
The value of the swap at the initiation date will be zero to both parties. For this statement to be true, the values of the cash flow streams that the swap parties are going to exchange should be equal. Let's illustrate this concept with a hypothetical example in which the value of the fixed leg and floating leg of the swap will be Vfix and Vfl respectively. Thus, at initiation:
Vfix =Vfl
Notional amounts are not exchanged in interest rate swaps because these amounts are equal and it does not make sense to exchange them. If we assume that parties also decide to exchange the notional amount at the end of the period, the process will be similar to an exchange a fixed rate bond and floating rate bond with the same notional amount. Therefore we can value swap contracts in terms of fixed and floating rate bonds.
Let’s imagine that Apple decides to enter a 1-year, fixed-rate receiver swap contract with quarterly installments on a notional amount of $2.5 billion while Goldman Sachs is the counterparty for this transaction that provides fixed cash flows which determine the fixed rate. Assume the USD LIBOR rates are the following:
Let’s denote the annual fixed rate of the swap by c, the annual fixed amount by C and the notional amount by N.
so if we denote DFi for i-th maturity, we will have the following equation:
which in turn can be re-written as:
Where q is the frequency of swap payments in a year.
We know that in interest rate swaps, parties exchange fixed and floating cash flows based on the same notional value. Thus, the final formula to find fixed rate will be:
A wide variety of swaps are utilized in finance in order to hedge risks, including interest rate swap,asset swap, and currency swaps. An interest rate swap is a contractual agreement between two parties agreeing to exchange cash flows of an underlying asset for a fixed period of time. The two parties are often referred to as counterparties and typically represent financial institutions. Vanilla swaps are the most common type of interest rate swaps. These convert floating interest payments into fixed interest payments and vice versa.
How Is the Fixed Rate Determined?
The value of the swap at the initiation date will be zero to both parties. For this statement to be true, the values of the cash flow streams that the swap parties are going to exchange should be equal. Let's illustrate this concept with a hypothetical example in which the value of the fixed leg and floating leg of the swap will be Vfix and Vfl respectively. Thus, at initiation:
Vfix =Vfl
Notional amounts are not exchanged in interest rate swaps because these amounts are equal and it does not make sense to exchange them. If we assume that parties also decide to exchange the notional amount at the end of the period, the process will be similar to an exchange a fixed rate bond and floating rate bond with the same notional amount. Therefore we can value swap contracts in terms of fixed and floating rate bonds.
Let’s imagine that Apple decides to enter a 1-year, fixed-rate receiver swap contract with quarterly installments on a notional amount of $2.5 billion while Goldman Sachs is the counterparty for this transaction that provides fixed cash flows which determine the fixed rate. Assume the USD LIBOR rates are the following:
Let’s denote the annual fixed rate of the swap by c, the annual fixed amount by C and the notional amount by N.
so if we denote DFi for i-th maturity, we will have the following equation:
which in turn can be re-written as:
Where q is the frequency of swap payments in a year.
We know that in interest rate swaps, parties exchange fixed and floating cash flows based on the same notional value. Thus, the final formula to find fixed rate will be:
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