The interest rate diffusion refers to the Brace-Gatarek-Musiela (BGM) model that is a multi-factor log-normal model. The model is used for pricing interest rate and FX derivatives. The method directly models the movement of the whole yield curve through the dynamics of correlated spanning forward LIBOR rates. This feature gives the BGM model much more flexibilities to model the correlation among the rates on the whole yield curve.

Calculation of the Greeks in the local volatility model is difficult because recalibrating the local volatility surface tends to result in high numerical error terms. While this appears to be OK for first order Greeks, for higher order Greeks we are forced to make some approximations.

The Canada Housing Trust (“CHT”) will raise funds by issuing Canada Mortgage Bonds and use the proceeds to purchase VRMBS’s from Approved Sellers. For each VRMBS purchased CHT will also enter into a swap, where it pays the MBS interest and reinvestment income to the swap counterparty and receives fixed coupon cashflows, which are used to service the CMB. CHT will also pay CMHC an up-front guarantee fee for each CMB issuance. In return CMHC provides a guarantee for the CMB’s.

The purpose of the credit risk calculator is to ensure that the expected loss that can occur from the guarantor’s (CMHC’s) perspective is covered by the guarantee fee. From CMHC’s perspective, the risk of loss will occur if an AAA/AA swap counterparty fails instantaneously without any rating migration to a lower state (i.e., AA to A). Under a normal rating migration, the swap counterparty to the Trust would have to collateralize its exposure.