What's new

# P1.T3.511. Prepayment modeling and Monte Carlo simulation (Tuckman)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning outcomes: Explain prepayment modeling and its four components: refinancing, turnover, defaults, and curtailments. Describe the steps in valuing an MBS using Monte Carlo Simulation. Define Option Adjusted Spread (OAS), and explain its challenges and its uses.

Questions:

511.1. According to Tuckman, "A prepayment model uses loan characteristics and the economic environment (i.e., interest rates and sometimes housing prices) to predict prepayments. The most common practice identifies four components of prepayments, namely, in order of importance, refinancing, turnover, defaults, and curtailments. These components are typically modeled separately and their parameters estimated or calibrated so as to approximate available historical data." (Source: Bruce Tuckman, Angel Serrat, Fixed Income Securities: Tools for Today’s Markets, 3rd Edition (New York: Wiley, 2011))

About these four components, each of the following is true EXCEPT which is false?

a. Refinancing is often modeled with an incentive function for a pool or group of loans in a pool, and then prepayments due to refinancing are defined as a nondecreasing function of that incentive; an example of an incentive function is I = [WAC - R]*WALS*A-K
b. Turnover is primarily a function of interest rates and tends to be independent of seasonality but highly responsive to the so-called media effect
c. Defaults are a source of prepayments in the sense that mortgage guarantors pay interest and principal outstanding when a borrower defaults
d. Curtailments are partial prepayments by a particular borrower. These tend to be most important when loans are older and balances are low

511.2. According to Tuckman, the valuation of a mortgage-backed security (MBS) is well-suited to a Monte Carlo simulation because the model can incorporate each of the following features EXCEPT which of these is difficult for the Monte Carlo simulation?

a. Path-dependent cash flows
b. Burnout and media effects
c. Measures of interest rate sensitivity
d. American- or Bermuda-style options

511.3. Tuckman writes that the "Option Adjust Spread (OAS) is the most popular measure of relative value for MBS." (Source: Bruce Tuckman, Angel Serrat, Fixed Income Securities: Tools for Today’s Markets, 3rd Edition (New York: Wiley, 2011))

In the context of a Monte Carlo valuation of a mortgage-backed security (MBS), each of the following is true about the OAS EXCEPT which is false?

a. If the assumption for interest rate volatility increases in the MBS Monte Carlo valuation model, then the OAS should increase also
b. To the extent that the MBS Monte Carlo valuation model accounts correctly for scheduled cash flows and prepayments, the OAS represents the deviation of a security’s market price from its fair value
c. The practical challenge of using models and OAS to measure relative value is in determining when OAS really does indicate relative value and when it indicates that the model is misspecified
d. Because the MBS Monte Carlo valuation model is supposed to account completely for the effects of interest rates on cash flows and discounting, the OAS should be uncorrelated with interest rate movements