Debt Convexity Analytic

From Open Risk Manual

Definition

Debt Convexity Analytic. The second derivative of a security's price with respect to its yield, divided by the security's price. A security exhibits positive convexity when its price rises more for a downward move in its yield than its price declines for an equal upward move in its yield. Further notes: A measure of the change in price for a given change in Modified Duration. This always (necessarily) refers to Modified Duration. This is used as another risk measurement. Numerator is always (a) duration - either MacCaulays or Modified. Always rate of change of (one of the) Duration against some other parameter. The other paramater can be characterised as a Yield (it may be the Price, but that has a relationship to the Yield in any case). REVIEW: Inconsistency in the above - is it always necessarily Modified Duration that is referred to, or "any" Duration measure (Macaulays and.or Modified)? notes 9 Dec A measure of the sensitivity of the price with reference to interest rates. This is normally determined with reference to maturity, but since there are different maturity dates, this figure gives an estimate of the equitvalent if you had a homogenous portfolio, i.e. this is an estimate based on a pure equivalent, homogenous portfolio. Convexity of instrument versus portfolio. Sees instrument in terms of the set of cashflows. The term Convexity can be applied either to a bond or to a portfolio. More notes: When you get Convexit in MD, it will tell you what Duration it is refrfering to, along with Redemption Date (logically). Also if there is Option Adjusted Yield, there is a third set of analytics. What are they? i.e. OA Convexity, Duration Yield and the rest. Conclusions: Agreed to revisit this in OTC.


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