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t. e. In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
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.
Stock duration. The duration of a stock is the average of the times until its cash flows are received, weighted by their present values. The most popular model of duration uses dividends as the cash flows. In vernacular, the duration of a stock is how long we need to receive dividends to be repaid the purchase price of the stock.
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.
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.
Duration gap. In Finance, and accounting, and particularly in asset and liability management (ALM), the duration gap is the difference between the duration - i.e. the average maturity - of assets and liabilities held by a financial entity. [1] A related approach is to see the "duration gap" as the difference in the price sensitivity of interest ...
e. Lanchester's laws are mathematical formulas for calculating the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. [1][2] In 1915 and 1916 during World War I, M. Osipov [3 ...
Newton's method in optimization. A comparison of gradient descent (green) and Newton's method (red) for minimizing a function (with small step sizes). Newton's method uses curvature information (i.e. the second derivative) to take a more direct route. In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding ...