A securitization is a financial transaction in which assets are pooled and securities representing interests in the pool are issued. An example would be a financing company that has issued a large number of auto loans and wants to raise cash so it can issue more loans. One solution would be to sell off its […]

Efficient Frontier

The efficient frontier was first defined by Harry Markowitz in his groundbreaking (1952) paper that launched portfolio theory. That theory considers a universe of risky investments and explores what might be an optimal portfolio based upon those possible investments. Consider an interval of time. It starts today. It can be any length, but one-year is typically assumed. Today’s […]


Callable Bond

A callable bond (or redeemable bond) is a bond whose indenture includes one or more call provisions providing for the early retirement (“call” or “redemption”) of the bond. Call provisions may provide for optional redemption, extraordinary redemption or sinking fund redemption. When included in a bond’s indenture, extraordinary and sinking fund redemption are “boiler plate” provisions that usually afford the issuer little opportunity to benefit at investors’ expense. Form […]

Bankers Acceptance

A bankers acceptance (BA) is a money market instrument: a short-term discount instrument that usually arises in the course of international trade. Before we explain BAs, let’s introduce some more basic concepts. A draft is a legally binding order by one party (the drawer) to a second party (the drawee) to make payment to a third party (the payee). A simple example […]

Futures Contract

A futures contract (or future) is an exchange-traded derivative which is similar to a forward. Both futures and forwards represent—or emulate financial consequences of—an agreement to buy/sell a notional amount of some underlying asset on some future date, for an agreed-upon price. Both can be for physical settlement or cash settlement. Both offer a convenient […]

<strong>Exhibit 2:</strong> Cash flows—servicing fees, principal and interest—are illustrated for a mortgage pass-through at PSAs 50%, 100% and 150%. Collateral is 30-year fixed-rate mortgages paying an average mortgage rate of 9.5%. Service fees are 0.5%.


Many forms of consumer debt, such as home mortgages, credit card debt and auto loans, permit the borrower to pay down the indebtedness at an accelerated rate or to retire the debt early with a single payment. If a homeowner decides to sell her home, she will use the proceeds of the sale to retire […]

With an IO and PO CMO structure, all interest cash flows go to the IO. All principal cash flows go to the PO. The shape of the region indicating principal payments is determined by the rate at which underlying mortgages prepay. This exhibit assumes 30-year fixed mortgages, most of which typically prepay within ten or fifteen years.

Interest Only & Principal Only CMOs

Interest only (IO) and principal only (PO) CMO bonds are obtained by stripping the interest cash flows from the principal cash flows of mortgage collateral. The interest cash flows form one bond, which is the IO. The principal cash flows form a second bond, which is the PO. This is illustrated in Exhibit 1. Prepayment […]

Oil forward curve

Forward Contract

A forward contract—or forward—is an OTC derivative. In its simplest form, it is a trade that is agreed to at one point in time but will take place at some later time. For example, two parties might agree today to exchange 500,000 barrels of crude oil for USD 92.08 a barrel three months from today. […]

Inverse Floater

An inverse floater (or reverse floater) is a floater whose coupon fluctuates inversely with its reference rate. For example, an inverse floater linked to Libor would have a floating coupon that increased when Libor decreases and decreased when Libor increased. With each coupon payment, an inverse floater’s floating rate is reset for the next period […]

Intensity Model

Intensity Model

Intensity models (also called reduced form models) are a form of default model. Lets start by considering what are known as mortality models of default. These are essentially a discrete form of intensity model. Once we have established them, we will take a limit as time intervals go to zero—and out will pop intensity models. […]

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