# Pricing and Valuing a Plain Vanilla Interest Rate Swap

• The price of a plain vanilla interest rate swap is quoted as the fixed rate side; never forget that the value of a swap is not the same as the price.
• In order to find the appropriate fixed rate for the interest rate swap's price, the swap can be viewed as a combination of bonds.

## Pricing an Interest Rate Swap

• The coupon rate that equates the value of the fixed rate bond to the value of the floating rate bond must be calculated in order to set the swap value equal to zero at inception.
• The value of the floating rate bond will be par at inception and at each coupon reset date.
• Calculating the fixed rate that will set the initial value of the swap to zero:

FS(0,n,m) = 1.0 - B0(hn) / SB0(hj)

• FS(0,n,m) = The fixed rate on the swap
• B0(hn) = The present value factor for the hypothetical notional principal payment of 1.0.
• B0(hj) = The present value factor for each interest rate payment; this factor is based on the expected floating rate payments in the future.
• The interest rate calculated by this formula will need to be annualized in order to get the swap's price (i.e., if the calculation for a swap that pays every six months generates an answer of 0.025, then the swap's price is 5%)
• This method must be practiced. Candidates can start by walking through and/or practicing problems open book to obtain better understanding and then gradually easing to closed book practice. CFAI may require candidates to price the fixed rate on a plain vanilla interest rate swap on the exam.

## Valuing an Interest Rate Swap

• Most likely, the value of a plain vanilla interest rate swap will only equate to zero at initiation, as interest rates will change over the life of the swap.
• In order to value the swap, an analyst will need to value corresponding fixed and floating rate bonds based on current market place interest rates.

Value of a Swap (fixed rate receiver) = Value of Equivalent Fixed Rate Bond - Value of Equivalent Floating Rate Bond

Value of a Swap (floating rate receiver) = Value of Equivalent Floating Rate Bond - Value of Equivalent Fixed Rate Bond

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