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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 ...
In practice the most significant of these is bond convexity, the second derivative of bond price with respect to interest rates. As the second derivative is the first non-linear term, and thus often the most significant, "convexity" is also used loosely to refer to non-linearities generally, including higher-order terms.
On the other hand, a bond with call features - i.e. where the issuer can redeem the bond early - is deemed to have negative convexity as rates approach the option strike, which is to say its duration will fall as rates fall, and hence its price will rise less quickly. This is because the issuer can redeem the old bond at a high coupon and re ...
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.
Convexity (finance), second derivatives in financial modeling generally; Convexity in economics; Bond convexity, a measure of the sensitivity of the duration of a bond to changes in interest rates; Convex preferences, an individual's ordering of various outcomes
Upon default the bonds have a recovery rate of 30% Under these conditions the 95% VaR for holding either of the bonds is 0 since the probability of default is less than 5%. However if we held a portfolio that consisted of 50% of each bond by value then the 95% VaR is 35% (= 0.5*0.7 + 0.5*0) since the probability of at least one of the bonds ...
In simple terms, a convex function graph is shaped like a cup (or a straight line like a linear function), while a concave function's graph is shaped like a cap . A twice- differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain . [ 1 ]
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 usually preferred. The discussion of the "negative convexity" and "option cost" of a bond is essentially a discussion of a single MBS feature (rate-dependent cash flows) measured in different ways.