Swap Average Term

The average term is calculated for a swap that underlies a European style payer swaption, which is in the calibration portfolio for a Bermudan swaption with amortizing notional (i.e., the outstanding notional is reduced from time-to-time). Given the payer swaption maturity and the average swap term pair, we then look up, from a table indexed by payer swaption maturity and underlying swap term, the corresponding Black’s implied volatility.

The Black’s volatility is then applied to compute the market price for the payer swaption above; this market price is required to calibrate the short-rate volatility for pricing the Bermudan swaption above.

We consider a single currency Bermudan style swaption, which has underlying swap specified as follows,

Consider a European style payer swaption, which is in the calibration portfolio for the Bermudan swaption in Section 2. In particular assume that the payer swaption has maturity

Given the swaption maturity and average swap term pair, and , for the payer swaption above, we then look up, from a table indexed by payer swaption maturity and underlying swap term, the corresponding Black’s implied volatility. The Black’s volatility is then applied to compute the market price for the payer swaption above; this market price is required to calibrate the short-rate volatility for pricing the Bermudan swaption.

We recommend, for operational robustness, that we include a check that the resulting average swap term is positive; if the average swap term is non-positive, an exception should be raised and handled.

Swap Average Term

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