We calculate the Treasury transfer coupon rate, in the case of zero coupon payment frequency, or the equivalent annualized simple rate in the case of non-zero coupon payment frequency, from which the transfer coupon rate.

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.

There is one theoretical subtlety about multi-currency models. Risk-neutral probabilities differ in both currencies, because numeraires are different. In the domestic risk-neutral probability, the expectation of the daily discounted value of a unit of domestic currency is equal to the domestic discount factor:

The generated simulation must satisfy certain requirements. These properties fall into two categories. First, there are no arbitrage conditions, which are to be satisfied exactly. Second, there is a requirement to reproduce input calibration data as accurately as possible with selected types of analytical parameterizations of model parameters.