金融工程是一个多学科交叉的领域涵盖从财经，数学，统计，工程和数值计算方法。FE&RM Part 1 这门课的重点会放在是用简单随机模型来给包括股票，固定收益工具，信用以及抵押支持证券在内的各种资产类别衍生品证券定价。我们也将思考其中证券在金融危机中的角色。这门课程一个引人注目的特别栏目是对Emanuel Derman （著名“宽客”，畅销书“宽客人生”的作者）的一段采访。我们希望完成这门课的学生将能够开始理解金融工程背后的高深原理。但更重要的是，我们希望你们也能理解这一理论在实践上的局限性以及明白为什么总是应该用批判的眼光看待金融模型。接下来的FE&RM Part 2将会进一步深入学习衍生品定价模型但是它也会关注资产配置和资产组合优化以及其他金融工程的应用实例，像实物期权，商品衍生品，能源衍生品和程序化交易。
Mortgage Pass-Throughs in Excel
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来自 Columbia University 的课程
金融工程与风险管理，第 1 部分
1370 个评分
从本节课中
Introduction to Mortgage Mathematics and Mortgage-Backed Securities
Basic mortgage mathematics; mechanics of mortgage-backed securities (MBS) including pass-throughs, principal-only and interest-only securities, and CMOs; pricing of MBS; MBS and the financial crisis.
与讲师见面
Martin HaughCo-Director, Center for Financial Engineering
Industrial Engineering & Operations Research
Garud IyengarProfessor
Industrial Engineering and Operations Research Department
In this module we're going to go through the mechanics of mortgage pass through
securities. And we will do that within the context of
our Excel spreadsheet, which I hope you have with you.
You can download that Excel spreadsheet with these modules and mortgage backed
securities. We're going to look at the second
worksheet in this Excel workbook. It's going to be about mortgage pass
throughs. We'll discuss the mechanics of mortgage
pass throughs. And see how the, how the cash flows of a
mortgage pass through are created, and passed on to investors.
The second worksheet on the XL workbook that goes along with these modules, and
mortgages, and mortgage backed securities is called pass through.
This worksheet shows the mechanics of a simple pass through mortgage backed
security. Now, I just want to state in advance.
Don't worry too much if it takes you some time to figure out.
What the various self formulas are doing. it's not a hugely important part of this
course. What I want you to come away with is a
basic understanding of the mechanics of how these kinds of securities work.
So what we have here is the following. We've assumed that the pass through.
Now remember, a pass through mortgage backed security is constructed.
From a pool of underlying mortgage loans. So we might assume, for example, that the
mortgage balance, or here, the remaining mortgage balance, is 400.
That might represent $400 million for example, representing a large pool of
underlying mortgages. We're going to assume that the mortgage
rate, so if you like, this is the coupon rate on the underlying mortgages.
It's 8.125%. The pass through rate is 7.5%.
Now, what is the difference between these 2 rates?
Well, the pass through rate is the rate that gets passed on to investors.
And it will always be less than the mortgage rate.
And that difference accounts for the fees associated with servicing.
The mortgage-backed security, in this case the pass-through.
Somebody has to organize and manage and service the mortgage-backed securities.
They need to be paid a fee for doing so. That fee is represented by the difference
between the mortgage rate, 8.125%, And the pass thru rate 7.5%.
The initial monthly payment, or if you like, the average monthly payment, that
the underlying mortgage owners are paying, is 24.989.
The seasoning, so this is how old the mortgage pool currently is, it's 3
months,and the term of the loan of the underlying mortgages is assumed to be 20
months. Now of course this is very unrealistic in
realty you would be in a much larger pool certainly for mortgages or mortgage
backed securities that have just been initiated.
But I've assumed 20 months here, just so that we can see all of the payments on
one screen. In reality, this might start off as being
240 or 360, corresponding to 20 or 30 year loans, respectively.
We start off in Month 1, and let's work across.
So, we have our conditional prepayment rates.
So, this is our CPR, which is expressed as an annual rate.
It tells you what percentage of the outstanding mortgage at the beginning of
the period will be prepaid. Of course, we will need convert this into
a single month mortality rate, and that's what we do here.
The SMM gives us the percentage of the mortgage balance that is prepaid that
month. We have an initial beginning monthly
balance of 400. The monthly payment is 24.989 as we
caluculated earlier. This is the monthly interest paid in by
mortgage holders. And this is the monthly interest paid out
to the past through investors. Note that this interest.
Payment here 2.5 is less then 2.71 and that's because of the difference 8.125%
and 7.5%. Finally the scheduled principle repayment
is 22.281. That's equal to E13 minus F13.
So that's the monthly payment minus the monthly interest paid in.
And then finally there are some prepayments.
As I mentioned in the last module. Sometimes mortgage owners prepay, and
they might do so for various reasons. Maybe they're selling their house and
moving to another location, maybe they've gotten divorced, maybe they've had a
flood or a fire, maybe they've defaulted on their payments.
And all those situations What the mortgage investors see, investors in
mortgage-backed securities see is the mortgage being prepaid.
So we're going to assume that these prepayments take place according to this
schedule, the cpr. And SMM schedule and we get a prepayment
of 2.53. So therefore the total principle payment
is .253 plus 22.281 and that gives us 22.533.
We can therefore subtract that from the initial mortgage balance of 400 to give
an ending mortgage balance of 377.47. We then move on to the next time period,
time period two. We see that the conditional pre-payment
rate is increased to one percent. We get our single monthly mortality rate
and so on. We know our beginning monthly balance is
377, this is the same monthly balance we had at the end of the previous period.
We get our monthly payment. Now notice our monthly payments are now
no longer the same constant. So in our last module we had a constant B
being paid in every period. We would've the same constant B being
payed in every period here, if there were no prepayments.
But there are prepayments. Those prepayments actually reduce the
outstanding principle by more than what you'd expect.
And therefore that changes the B in each period.
So if you, if you look carefully at the formulas here, you'll see that this
formula is the same formula we assume to calculate B.
In our earlier module. But of course we have to keep
recalculating it in every period to adjust for the fact that prepayments are
taking place. So what I want you to get from this
spreadsheet is basically just how the repayments are calculated.
How the interest payments are calculated. The interest payments paid out to past
due investors are calculated. And the fact that prepayments take place
and that these prepayments Alter the outstanding mortgage principal that
remains at the end of every period. Now this is an idealized world, we don't
have any defaults. We don't have any randomness in our
prepayments. We're assuming prepayments occur
according to this deterministic schedule given to us by the CPR.
That's all fine as I said. In the real world of course You have to
take these into account, but for our purposes we just want to understand some
of the mechanics behind how these mortgage backed securities are created.
And the simplest type of mortgage backed security is what is called the mortgage
pass through. Where you just pool a whole series of
loans together and then you pay out the principle and interest on those loans out
to the investors in the pass through security.
