Pricing Defaultable Instruments

In risky bond pricing, the recovery in the event of default is only applied to the coupon amount (i.e. recovery of treasury); while the recovery of par assumption is generally more commonly used. However, the impact analysis shows that the impact of applying either assumption in the calibration of incremental spreads is small.

The prepayment rate due to refinancing follows an S-shaped function of refinancing incentive. Refinancing is typically zero when rates are above the pool's rate, picks up as rates drop, and tops out at some maximum level (because not everyone can refinance).

Mortgage prepayment and liquidation are deterministic. The mortgages in the MBS pool behave identically in terms of prepayment and liquidation.

Partial prepayment rate and liquidation rate are functions of the refinancing incentive, burnout factor, and seasoning of the pool.

For the Black-Derman-Toy (BDT) arbitrage-free binomial tree, the Black implied volatility for caplets can correspond one-to-one to the volatility of the short rate. The impact analysis results show that the caplet implied volatility can well approximate the volatility of the time dependant interest rate. Therefore, due to its computational simplicity, the BDT framework is acceptable for spread calibration.

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