Let Ti, i=1, … ,n be a set of dates, on which payments of the floating...

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, ri 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).

2) 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).

How to address the question （2）

Solutions

Expert Solution

1) Businesses uses different type of Swap to get himself hedged.

Swap rate help to lock in and fixed future..SFR rate is the rate which one party agree to pay in return of Uncertain or floating rate .

Formula for arriving SFR swap fixed rate is

= (1 - last Discounting factor) / Total Present value factor..

By deriving this fixed rate there is no difference between the Fixed rate payer and floating rate payer...Both are on same platform.

2) Swap rate is the rate which makes Floating and fixed side equal.

That means If fixed side is the same as derive using the above formula then floating rate payer and floating rate reciever is in no benefit initially and value of swap to be found as zero.

I.e Value of floating rate payer = Value of floating rate receiver.

This situation only happens initially when swap is entered by both party. After swap initiation, value changes in between and one party is in advantage over other due to floating rate fluctuation .

jeff jeffy answered 1 month ago

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