Option-adjusted spread
Encyclopedia
Option adjusted spread is the flat spread
which has to be added to the treasury
yield curve
in a pricing model (that accounts for embedded options) to discount a security
payment to match its market price
. OAS is hence model dependent. This concept can be applied to a mortgage-backed security
(MBS), option
, bond
and any other interest rate derivative
. In the context of an MBS, the option relates to the right of property owners, whose mortgages back the MBS, to prepay the full mortgage amount.
" measurement of bond premium over a pre-determined cash-flow model, the OAS describes the market premium over a model including two types of volatility
:
Designing such models in the first place is complicated because prepayment variations are a behavioural function of the stochastic
interest rate. (They tend to go up as interest rates come down.)
OAS is an emerging term with fluid use across MBS finance
. The definition here is based on Lakhbir Hayre's Mortgage Backed Securities text book. Other definitions are rough analogs:
Treasury bonds may not be available with maturities exactly matching likely cash flow payments so some interpolation
may be necessary to make this calculation.
-payers will only tend to exercise this right when it is favourable for them and unfavourable for the bond-holder, buying an MBS partly involves selling an option
. This is the source of the difference between the option adjusted spread (OAS) and the Z-spread (which ignores embedded options).
Since prepayments rise as interest rate
s fall and vice versa, the basic (pass-through) MBS has negative bond convexity
(second derivative of price over yield
). The MBS-holder's exposure to property-owner prepayment has several names:
This difference in convexity can also be used to explain the price differential from an MBS to a treasury bond. However, the OAS-figure is typically preferred. The discussion of the "negative convexity" and "option adjusted spread" on a bond is essentially a discussion of a single MBS feature (prepayment risk) measured in different ways.
Yield spread
In finance, the yield spread is the difference between the quoted rates of return on two different investments, usually of different credit quality.It is a compound of yield and spread....
which has to be added to the treasury
Treasury security
A United States Treasury security is government debt issued by the United States Department of the Treasury through the Bureau of the Public Debt. Treasury securities are the debt financing instruments of the United States federal government, and they are often referred to simply as Treasuries...
yield curve
Yield curve
In finance, the yield curve is the relation between the interest rate and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. For example, the U.S. dollar interest rates paid on U.S...
in a pricing model (that accounts for embedded options) to discount a security
Security (finance)
A security is generally a fungible, negotiable financial instrument representing financial value. Securities are broadly categorized into:* debt securities ,* equity securities, e.g., common stocks; and,...
payment to match its market price
Price
-Definition:In ordinary usage, price is the quantity of payment or compensation given by one party to another in return for goods or services.In modern economies, prices are generally expressed in units of some form of currency...
. OAS is hence model dependent. This concept can be applied to a mortgage-backed security
Mortgage-backed security
A mortgage-backed security is an asset-backed security that represents a claim on the cash flows from mortgage loans through a process known as securitization.-Securitization:...
(MBS), option
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
, bond
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
and any other interest rate derivative
Interest rate derivative
An interest rate derivative is a derivative where the underlying asset is the right to pay or receive a notional amount of money at a given interest rate...
. In the context of an MBS, the option relates to the right of property owners, whose mortgages back the MBS, to prepay the full mortgage amount.
Definition
In contrast to the simple "yield curve spreadYield curve spread
- In Economics :* Yield curve - The spread between long-term and short-term Treasuries* Z-spread - Also known as yield-spread curve, the flat spread over the treasury yield curve- In Materials Science :...
" measurement of bond premium over a pre-determined cash-flow model, the OAS describes the market premium over a model including two types of volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
:
- Variable interest rateInterest rateAn interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...
s - Variable prepayment rates.
Designing such models in the first place is complicated because prepayment variations are a behavioural function of the stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
interest rate. (They tend to go up as interest rates come down.)
OAS is an emerging term with fluid use across MBS finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
. The definition here is based on Lakhbir Hayre's Mortgage Backed Securities text book. Other definitions are rough analogs:
- Take the expected valueExpected valueIn probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
(mean NPVNet present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
) across the range of all possible rate scenarios when discounting each scenario's actual cash flows with the treasury yield curve plus a spread, X. The OAS is defined as the value of X equating the market price of the MBS to its value in this theoretical framework.
Treasury bonds may not be available with maturities exactly matching likely cash flow payments so some interpolation
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
may be necessary to make this calculation.
Convexity
The word 'Option' in Option adjusted spread relates to the right of property owners, whose mortgages back the MBS, to prepay the full mortgage amount. Since mortgageMortgage loan
A mortgage loan is a loan secured by real property through the use of a mortgage note which evidences the existence of the loan and the encumbrance of that realty through the granting of a mortgage which secures the loan...
-payers will only tend to exercise this right when it is favourable for them and unfavourable for the bond-holder, buying an MBS partly involves selling an option
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
. This is the source of the difference between the option adjusted spread (OAS) and the Z-spread (which ignores embedded options).
Since prepayments rise as interest rate
Interest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...
s fall and vice versa, the basic (pass-through) MBS has negative bond convexity
Bond convexity
In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates . In general, the higher the convexity, the more sensitive the bond price is to decreasing interest rates and...
(second derivative of price over yield
Yield (finance)
In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return...
). The MBS-holder's exposure to property-owner prepayment has several names:
- extension or contraction risk
- prepayment risk
- reinvestment riskReinvestment riskReinvestment risk is one of the main genres of financial risk. The term describes the risk that a particular investment might be canceled or stopped somehow, that one may have to find a new place to invest that money with the risk being there might not be a similarly attractive investment available...
This difference in convexity can also be used to explain the price differential from an MBS to a treasury bond. However, the OAS-figure is typically preferred. The discussion of the "negative convexity" and "option adjusted spread" on a bond is essentially a discussion of a single MBS feature (prepayment risk) measured in different ways.
See also
- Z-spreadZ-SpreadThe Z-spread, ZSPRD or Yield curve spread on a simple mortgage-backed security is the flat spread over the treasury yield curve required in discounting a pre-determined coupon schedule to arrive at its present market price....
- I-spreadI-spreadThe Interpolated Spread or I-spread or ISPRD is the difference between the yield to maturity of the bond and the linearly interpolated yield to the same maturity on an appropriate reference curve....
- Convertible bondConvertible bondIn finance, a convertible note is a type of bond that the holder can convert into shares of common stock in the issuing company or cash of equal value, at an agreed-upon price. It is a hybrid security with debt- and equity-like features...
s must pay a similar increased yield (over the standard corporate bond) when they are callable by the issuing company. - Monte CarloMonte Carlo methodMonte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
techniques are used to derive the Option adjusted spread.
External links
- The Society of Actuaries review of the application of OAS to insurance, and other option adjustments. Society of ActuariesSociety of ActuariesThe Society of Actuaries is a professional organization for actuaries based in North America. It was founded in 1949 as the merger of two major actuarial organizations in the United States: the Actuarial Society of America and the American Institute of Actuaries...
.