>Blog>CFA Fixed Income: Mortgage Backed Securities and Its Pricing

# CFA Fixed Income: Mortgage Backed Securities and Its Pricing

October 29, 2013

source: i.ytimg

### What is a Mortgage Backed Security?

According to Wikipedia:

“A mortgage-backed security (MBS) is a type of asset-backed security that is secured by … mortgages. The mortgages are sold to a financial institution … that "securitizes", or packages, the loans together into a security that can be sold to investors.”

In simplest scenario, MBS is a pass-through security where every month borrowers make principal and interest payments on their loans. These payments are collected by the financial institution that issued the MBS (or by a loan servicer) and investors in that MBS receive part these payments.

Mortgage-loans are similar to coupon paying bonds and hence are sensitive to interest rate environment. However, there are main two differences that make MBS interesting. Firstly, face values of these loans amortize over time and secondly, because of early payment option with the borrower, cash flows of these loans are not fully deterministic. The second difference, i.e. early payment option, makes pricing and valuation of MBSs challenging.

Here we will try to learn how an MBS is priced. The framework I have chosen in minimal to keep things simple. To price an MBS, at the minimum we need two components: an interest rate model and a prepayment model. Let’s dive into framework now.

### Interest Rate model

There is full range of interest rate model commonly categorized into short rate model and term-structure model. A short rate model, as name implies, forecasts short term rate (1-month for example). On the other hand, term-structure models for interest rates forecast all the points on the term-structure (1-month, 3-month, 1-year upto 30-years, for example).

Here we will use short-rate model called Vasicek model for interest rate (for details). The model is described by the following equation:

drt = a(b-rt)dt + σdWt

### Prepayment Model

While prepayment modeling often involves quite complex and sophisticated modeling, often at the loan level, here we are going to use a slightly modified approach based on Richard and Roll. The Richard and Roll prepayment model involves the following factors:

1. Refinancing incentive
2. Seasonality (month of the year)
3. Seasoning or age of the mortgage
4. Burnout

Richard and Roll propose a multiplicative model of the following:

CPR = RefIncentive * SeasonongMultiplier * SeasonalityMultiplier * BurnoutMultiplier

We will ignore Burnout Multiplier here and assume it to be 1.

### RefIncentive

Refi = .2406 – .1389 * arctan [ 5.952 * ( 1.089 – CouponRate / MortgageRate ) ]

Seasoning Multiplier

month 1= 1/30, month2=2/30…month30=30/30=1 and for all other months also factor=1

Seasonality Multiplier

For months Jan to Dec = [.94 .76 .73 .96 .98 .92 .99 1.1 1.18 1.21 1.23 .97];

Although as a first step we are using a simple prepayment model but let take some time and see what factors influence prepayments in details.

i) Loan-level variables: These are static variables decided at the time of origination like:

• Appraisal value,
• Loan Term,
• Loan-to-Value ratio,
• Purpose,
• Occupancy Type,
• Geographical Area
• FICO score of the borrower
• Spread at time of origination (SATO)
• Prepayment penalty and term

ii) Macro-economic variables: These are dynamic variables that are updated monthly like:

• 10 year interest rate
• Term spread defined by difference between long rate and short rate
• House Price Index (HPI)

iii) Derived variables: These are also dynamic and are calculated monthly like:

• Current house price
• Spread at time of origination (SATO)
• Current Loan-to-Value ratio (CLTV)
• Current coupon gap
• Change in HPI
• Performance history of the loan
• Seasoning
• Seasonality
• Principal fraction remaining

Each of these will be explained in the subsequent blogs in ‘R’ language. Stay tuned for more!

Get a detailed analysis and great insights into FICO score, SATO, LTV and audit chart relating to Mortagage Backed Securities in the next part of this blog.

EduPristine

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