Short for Asset-Backed Security. Also, a Public Securities Association standard model that defines an increasing sequence of monthly prepayment rates (SMM) that corresponds to to a constant absolute level of loan prepayments in all future periods. The formula for ABS is as follows:
Where Ft = The pool factor in period t
BALt = The amortized loan balance (as a fraction of par) of the pool in period t.
and AGEt = The weighted average loan age of the pool in period t.
An ABS speed can be converted directly into a sequence of SMM rates with the following formula:
SMM = (100*ABS) / (100 - ABS*(MONTH-1))
For more information, please see the Public Securities Association publication Standard Formulas for the Analysis of Mortgage-Backed Securities and Other Related Securities, page SF-13.
Balloon Mortgage:
A mortgage that amortizes like a typical level-pay mortgage until the balloon date, when all the remaining principal comes due. A typical balloon amortizes like a 30-year level-pay mortgage and has a balloon period of 5 to 7 years.
Convexity:
Convexity measures the change in duration, making it equal to the change in the change in price. This is known as a second-order term, and reflects the curvature of the price profile graph. The formula for effective convexity is:
(Price-dYield + Price+dYield -2*PriceBase)/(100*Yield2 *Price Base)
Coupon:
The periodic interest payment made to owners during the life of a bond. The coupon rate is the stated interest rate on the face of a bond.
CPR:
Constant Prepayment Rate: Prepayment expressed as an annual percentage of beginning period balance.
CPR = 100*(1.0 - (1.0- SMM/100)12).
DLL:
Dynamically Linked Library: A DLL is a library that is linked to applications at run-time rather than at compile time. Our DLLs allow calling applications to use our models, such as our prepayment model.
Duration:
Duration represents the percentage change in price for a basis point change in yield. This reflects the slope of the price profile graph. The formula for effective duration is:
(Price-dYield - Price+dYield)/(2 * dYield * PriceBase)
Hybrid Mortgage:
A mortgage that has a fixed interest rate for a set period, then becomes an ARM.
Incentive Curve:
Constant Prepayment Rate: Prepayment expressed as an annual percentage of beginning period balance.
CPR = 100*(1.0 - (1.0- SMM/100)12).
The S-shaped curve that shows the interest rate incentive to prepay. The ratio of the coupon rate to the current mortgage rate is shown on the x-axis and prepayment speed is on the y-axis. See illustration right.
Key Rate Duration:
Measures of duration and convexity rely on an assumption of parallel yield curve shifts. To take a more detailed look at interest rate risk, we may want to use a a method that examines risk along the entire yield curve. The method of key rate duration breaks down our traditional measure of duration into a series of partial durations. That is, we look at the effect of the change in each section of the yield curve on the price of a security. This lets us see what sections of the curve play the largest role in the price sensitivity of the security.
Lookback:
The number of days to "look back" when adjusting the interest rate. For example if a loan resets in July 2008, a lookback of 1 month would mean that the June 2008 index rate would be used in the calculation of the new coupon.
Mean Reversion:
Many analysts believe that in a well-defined interest-rate process, rates should not get "too high" or "too low." Although a simulation process may allow for interest rates to rise to very high levels or fall to next to nothing, experience suggests that persistent deviations of interest rates from historical ranges are not realistic. This notion of interest rates returning to long-term averages goes by the name of mean reversion. Within the confines of our OAS model, mean reversion has the effect of pushing the simulated rates closer to the implied forward rates based upon the initial term structure. In effect, this decreases volatility over time.
Net Life Cap:
The top potential coupon paid to the investor.
Net Life Floor:
The lowest potential coupon paid to the investor.
Par Rate:
The coupon rate currently being paid on a bond selling at par (face value).
Periodic Rate Collar:
The maximum amount at which the coupon paid to the borrower is allowed to change from one period to the next.
PSA Curve:
The theoretical prepayment model that shows the aging effect on prepayments. The PSA benchmark, denoted 100% PSA, assumes prepayments that start at .2% CPR in month one, and increase by .2% per month until month 30, when prepayments level off at 6% CPR. To interpret multiples of the PSA curve, simply multiply the entire curve by the amount by which you are scaling. For example, the 200% PSA curve starts at .4% CPR in month one and increases to 12% CPR by month 30.
OAS:
Option Adjusted Spread: The spread to short-term interest rates that equates the theoretical price of a bond to its market price. The OAS is a spread over all the short-term interest rate forecasts implied by the entire yield curve.
SMM:
Simple Monthly Mortality. Prepayment speed expressed as the percentage of the outstanding balance which prepays during a given month.
Tuning Factors:
Parameters that allow users to customize the way that the model behaves. All are normally 1.0 and in general values over 1 speed up prepayments, below one slow them down (steepness is a bit different).
Tuning Duration:
Similar to effective duration, but instead of price sensitivity to interest rates, price sensitivity to one of the tuning parameters is computed. This is accomplished by finding the price with the tuning parameter set to 1.05 times the original level, subtracting the price with the tuning parameter set to .95 times the original level, then dividing the result by the price with the tuning parameter set to 1.0 multiplied by 0.1 times the original level of the tuning parameter. The formula is :
(Pt*1.05 - Pt*.95)/(Pt * .1*t) where
t is the original level of the tuning factor and
Ps is the price of the security where the tuning factor is set to s.
WAC:
Weighted Average Coupon: The average coupon of a pool of mortgages weighted by outstanding balance.
WAL:
Weighted Average Life: The sum of the month number of each prepayment times the amount of the prepayment, all divided by the total prepayment. Divided again by 12 to annualize.
WAM:
Weighted Average Maturity: The remaining life of the loan. For a pool, the weighted average where the weights are the remaining balances of the constituent loans.
Zero or Spot Rate:
The current yield on a zero-coupon bond (a bond that makes no interest payments).
GLOSSARY
ABS:
Short for Asset-Backed Security. Also, a Public Securities Association standard model that defines an increasing sequence of monthly prepayment rates (SMM) that corresponds to to a constant absolute level of loan prepayments in all future periods. The formula for ABS is as follows:
ABS = 100 * (F1/F2 - BAL1/BAL2) / (AGE2*(F1/F2) - AGE1*(BAL1/BAL2))
Where Ft = The pool factor in period t
BALt = The amortized loan balance (as a fraction of par) of the pool in period t.
and AGEt = The weighted average loan age of the pool in period t.
An ABS speed can be converted directly into a sequence of SMM rates with the following formula:
SMM = (100*ABS) / (100 - ABS*(MONTH-1))
For more information, please see the Public Securities Association publication Standard Formulas for the Analysis of Mortgage-Backed Securities and Other Related Securities, page SF-13.
Balloon Mortgage:
A mortgage that amortizes like a typical level-pay mortgage until the balloon date, when all the remaining principal comes due. A typical balloon amortizes like a 30-year level-pay mortgage and has a balloon period of 5 to 7 years.
Convexity:
Convexity measures the change in duration, making it equal to the change in the change in price. This is known as a second-order term, and reflects the curvature of the price profile graph. The formula for effective convexity is:
(Price-dYield + Price+dYield -2*PriceBase)/(100*Yield2 *Price Base)
Coupon:
The periodic interest payment made to owners during the life of a bond. The coupon rate is the stated interest rate on the face of a bond.
CPR:
Constant Prepayment Rate: Prepayment expressed as an annual percentage of beginning period balance.
CPR = 100*(1.0 - (1.0- SMM/100)12).
DLL:
Dynamically Linked Library: A DLL is a library that is linked to applications at run-time rather than at compile time. Our DLLs allow calling applications to use our models, such as our prepayment model.
Duration:
Duration represents the percentage change in price for a basis point change in yield. This reflects the slope of the price profile graph. The formula for effective duration is:
(Price-dYield - Price+dYield)/(2 * dYield * PriceBase)
Hybrid Mortgage:
A mortgage that has a fixed interest rate for a set period, then becomes an ARM.
Incentive Curve:
Constant Prepayment Rate: Prepayment expressed as an annual percentage of beginning period balance.
CPR = 100*(1.0 - (1.0- SMM/100)12).
The S-shaped curve that shows the interest rate incentive to prepay. The ratio of the coupon rate to the current mortgage rate is shown on the x-axis and prepayment speed is on the y-axis. See illustration right.
Key Rate Duration:
Measures of duration and convexity rely on an assumption of parallel yield curve shifts. To take a more detailed look at interest rate risk, we may want to use a a method that examines risk along the entire yield curve. The method of key rate duration breaks down our traditional measure of duration into a series of partial durations. That is, we look at the effect of the change in each section of the yield curve on the price of a security. This lets us see what sections of the curve play the largest role in the price sensitivity of the security.
Lookback:
The number of days to "look back" when adjusting the interest rate. For example if a loan resets in July 2008, a lookback of 1 month would mean that the June 2008 index rate would be used in the calculation of the new coupon.
Mean Reversion:
Many analysts believe that in a well-defined interest-rate process, rates should not get "too high" or "too low." Although a simulation process may allow for interest rates to rise to very high levels or fall to next to nothing, experience suggests that persistent deviations of interest rates from historical ranges are not realistic. This notion of interest rates returning to long-term averages goes by the name of mean reversion. Within the confines of our OAS model, mean reversion has the effect of pushing the simulated rates closer to the implied forward rates based upon the initial term structure. In effect, this decreases volatility over time.
Net Life Cap:
The top potential coupon paid to the investor.
Net Life Floor:
The lowest potential coupon paid to the investor.
Par Rate:
The coupon rate currently being paid on a bond selling at par (face value).
Periodic Rate Collar:
The maximum amount at which the coupon paid to the borrower is allowed to change from one period to the next.
PSA Curve:
The theoretical prepayment model that shows the aging effect on prepayments. The PSA benchmark, denoted 100% PSA, assumes prepayments that start at .2% CPR in month one, and increase by .2% per month until month 30, when prepayments level off at 6% CPR. To interpret multiples of the PSA curve, simply multiply the entire curve by the amount by which you are scaling. For example, the 200% PSA curve starts at .4% CPR in month one and increases to 12% CPR by month 30.
OAS:
Option Adjusted Spread: The spread to short-term interest rates that equates the theoretical price of a bond to its market price. The OAS is a spread over all the short-term interest rate forecasts implied by the entire yield curve.
SMM:
Simple Monthly Mortality. Prepayment speed expressed as the percentage of the outstanding balance which prepays during a given month.
Tuning Factors:
Parameters that allow users to customize the way that the model behaves. All are normally 1.0 and in general values over 1 speed up prepayments, below one slow them down (steepness is a bit different).
Tuning Duration:
Similar to effective duration, but instead of price sensitivity to interest rates, price sensitivity to one of the tuning parameters is computed. This is accomplished by finding the price with the tuning parameter set to 1.05 times the original level, subtracting the price with the tuning parameter set to .95 times the original level, then dividing the result by the price with the tuning parameter set to 1.0 multiplied by 0.1 times the original level of the tuning parameter. The formula is :
(Pt*1.05 - Pt*.95)/(Pt * .1*t) where
WAC:
Weighted Average Coupon: The average coupon of a pool of mortgages weighted by outstanding balance.
WAL:
Weighted Average Life: The sum of the month number of each prepayment times the amount of the prepayment, all divided by the total prepayment. Divided again by 12 to annualize.
WAM:
Weighted Average Maturity: The remaining life of the loan. For a pool, the weighted average where the weights are the remaining balances of the constituent loans.
Zero or Spot Rate:
The current yield on a zero-coupon bond (a bond that makes no interest payments).