Pool & Rate Parameters
Prepayment & Market Dynamics
Spreads & Prepayment Metrics
- Option-Adjusted Spread (OAS): 112.4 bps
- Prepayment Option Cost: 32.6 bps
- Initial Prepayment Speed: 14.8% CPR (1.32% SMM)
- Total Pool Present Value: $101,421,850
Quantitative Visualizer
Dual 5x5 Stress & Sensitivity Analysis
Market Refi Rate vs WAC on CPR Speed (%)
Yield Shift vs PSA Speed on Duration (Years)
Monthly Amortization Schedule
| # | Age | Beg Balance ($) | Sched Prin ($) | Prepay Prin ($) | Net Interest ($) | Total CF ($) | CPR (%) | End Balance ($) |
|---|
Mathematical Foundations & Institutional Mechanics
1. Single Monthly Mortality (SMM) and Conditional Prepayment Rate (CPR)
Prepayment risk in mortgage pools is measured at two time scales: the annualized Conditional Prepayment Rate (\(\text{CPR}\)) and the monthly Single Monthly Mortality (\(\text{SMM}\)). The exact compounding relationship between them is:
Prepayment principal in any month \(m\) is calculated by multiplying \(\text{SMM}_m\) by the balance remaining after scheduled principal amortization: \(P_{\text{prep}, m} = (B_{m-1} - P_{\text{sched}, m}) \cdot \text{SMM}_m\).
2. Richard & Roll (1989, Goldman Sachs) Structural 4-Factor Model
Unlike static PSA benchmarks, the Richard & Roll framework models prepayment as a multiplicative interaction of four fundamental economic drivers:
- Refinancing Incentive (\(\text{RI}\)): Modeled via an arctan S-curve: \(\text{RI} = a + b \cdot \arctan(c \cdot (R_{\text{wac}} - R_{\text{mkt}}) - d)\). Inflection occurs when rate savings exceed 50–75 bps.
- Aging / Seasoning (\(\text{AGE}\)): Prepayments ramp up linearly over the first 30 months: \(\min(1.0, t / 30)\).
- Seasonality (\(\text{SEAS}\)): Prepayment activity surges in summer (peak June/July homebuying) and troughs in winter: \(1 + s_0 \cos(\frac{2\pi(m - 6)}{12})\).
- Burnout Effect (\(\text{BO}\)): As a pool experiences repeated refinancing waves, financially responsive borrowers exit, leaving behind inert mortgagors. Prepayment elasticity declines systematically.
3. Negative Convexity & Downward Concavity
For option-free fixed income instruments, the price-yield curve is convex (\(\frac{d^2 P}{dy^2} > 0\)), meaning prices rise faster when yields fall than they fall when yields rise. For MBS, the homeowner's embedded prepayment option creates negative convexity:
When interest rates drop, prepayments spike and principal is returned at par (\$100). The price appreciation is capped near par, causing the curve to curve concavely downward. Conversely, when rates rise, prepayments collapse, extending bond duration into an adverse market.
4. Option-Adjusted Spread (OAS) Decomposition
Because negative convexity is a structural disadvantage to the investor, institutional desks decompose the nominal Z-Spread into the true compensation (OAS) and the prepayment option cost: