Valuation of an Amortizing IRS

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Hi David,

Could you explain what is the motivation of Amortizing IRS?

And what is a step-by-step procedure to value them?

Many thanks,
Indira

 

[David Harper CFA FRM]

Hi Indira,

The primary hedging motivation is the same as a vanilla swap: to transform a fixed income (bond) asset/liability or hedge a fixed-income exposure.

A vanilla interest rat swap (e.g., the basis for the FRM study) transforms/hedges a so-called bullet bond: if a firm had a position in a bond that paid interest every six months but returned principal only at maturity, a vanilla IRS could transform fixed-to-floating or vice-versa; or could hedge the position.

However, if the underlying position were instead a mortgage backed security (or just a mortgage) with principal that amortizes, then an amortizing swap would match the exposure more directly. So the motivation is basically the same; what's different is that an amortizing IRS tends to be used to hedge (or transform the cash flows) MBS or otherwise amortizing exposure; i.e., the difference is the underlying exposure.

The valuation is essentially similar--we can still use either of Hull's approaches (value as two bonds; or discount the future expected net cash flows based on the forward curve)--the only difference is that the amortizing notional is included. I hope that helps, thanks,

 

[[email protected]]

Sounds clear now, thanks for the MBS example!

Hi Indira,

The primary hedging motivation is the same as a vanilla swap: to transform a fixed income (bond) asset/liability or hedge a fixed-income exposure.

A vanilla interest rat swap (e.g., the basis for the FRM study) transforms/hedges a so-called bullet bond: if a firm had a position in a bond that paid interest every six months but returned principal only at maturity, a vanilla IRS could transform fixed-to-floating or vice-versa; or could hedge the position.

However, if the underlying position were instead a mortgage backed security (or just a mortgage) with principal that amortizes, then an amortizing swap would match the exposure more directly. So the motivation is basically the same; what's different is that an amortizing IRS tends to be used to hedge (or transform the cash flows) MBS or otherwise amortizing exposure; i.e., the difference is the underlying exposure.

The valuation is essentially similar--we can still use either of Hull's approaches (value as two bonds; or discount the future expected net cash flows based on the forward curve)--the only difference is that the amortizing notional is included. I hope that helps, thanks,