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Contents. Duration (finance) In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change ...
In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life, [1][2][3] is the weighted average of the times of the principal repayments: it's the average time until a dollar of principal is repaid. In a formula, [4] where: is the time (in years) from the calculation date to payment . If desired ...
Option-adjusted spread (OAS) is the yield spread which has to be added to a benchmark yield curve to discount a security 's payments to match its market price, using a dynamic pricing model that accounts for embedded options. OAS is hence model-dependent. This concept can be applied to a mortgage-backed security (MBS), or another bond with ...
Bonds will have different yields and market returns based on the duration of the note, the issuer, the rate structure and more. A 10-year Treasury bond, for example, will have an entirely ...
Bond convexity is a measure of the sensitivity of the duration to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative); it is then analogous to gamma. In general, the higher the convexity, the more sensitive the bond price is to the change in interest rates.
For example, bonds can be readily priced using these equations. A typical coupon bond is composed of two types of payments: a stream of coupon payments similar to an annuity, and a lump-sum return of capital at the end of the bond's maturity—that is, a future payment. The two formulas can be combined to determine the present value of the bond.
The modified duration of a bond assumes that cash flows do not change in response to movements in the term structure, which is not the case for an MBS. For instance, when rates fall, the rate of prepayments will probably rise and the duration of the MBS will also fall, which is entirely the opposite behavior to a vanilla bond.
Because interest rate caps/floors are equivalent to bond puts and calls respectively, the above analysis shows that caps and floors can be priced analytically in the Hull–White model. Jamshidian's trick applies to Hull–White (as today's value of a swaption in the Hull–White model is a monotonic function of today's short rate). Thus ...