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Computing the Par Swap Rate (IRS)

The equilibrium forward swap rate, Fs is defined as the fixed swap rate that will equate the present value of the fixed and floating legs of the underlying swap. Using the definitions for the current value of a fixed and floating leg of a swap (see Introduction to Interest Rate Swaps), this means we wish to solve for the fixed rate (rfx) such that:

 

Equation Template

 

By rearranging this equation, an expression for the forward swap rate can be derived as:

 

Equation Template

 

 

The numerator in this expression is just the fair value of the floating leg, while the denominator is closely related to the fair value of the fixed leg.

 

In Resolution, the forward swap rate is therefore calculated using particular return values from the price functions for the fixed and floating leg. These can be generated by setting the appropriate output flag value in each of the pricing functions, as follows:

Price Function

Output Flag Value

Returned Value

 

.

 

_Price_FX

7

An array of two values. The first is the "Par Swap Rate Denominator", as described in the formula for the par swap rate. The second is the "Par Rate Notional Adjustment", an adjustment factor that is needed when the swap has an amortizing or accreting notional FV.

 

_Price_FL

3

The "Par Swap Rate Numerator", which in most cases is simply the fair value of the floating leg.

 

 

 

 

 

The par swap rate is then computed as:

 

Equation Template

 

 

See any of the IRS templates for a demonstration of how this procedure is implemented.

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