Valuation models

Residential whole loans

Two-factor paths of Hull-White rates and house prices; prepayments from turnover, seasonality, an age ramp and a refinancing S-curve with burnout; defaults rising with the current loan-to-value and falling with FICO; losses from the house value after foreclosure costs. Price from an OAS or OAS from a price, expected loss, effective duration and convexity, and yearly CPR, CDR and losses.

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Methodology

Conventions

  • Paths of Hull-White short rates and a lognormal house price index, correlated.
  • Prepayment: turnover with seasonality and an age ramp, plus a refinancing S-curve on the rate incentive, with burnout.
  • Default: a hazard rising with the current loan-to-value and falling with FICO; a default loses the balance less the house value net of costs, after liquidation.
  • Cash flows are discounted on each path plus the OAS; effective duration from a ±25bp curve shift.

References

  • Levin and Davidson (2005)
  • Hayre (2001)

Formulas

CDR
d₀ exp(β_LTV (LTV − 0.8) + β_F (700 − FICO)/100)
Loss
max(0, B − (1 − k) H)