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Fixed income inquiry on duration formula

Does the duration formula (V subscript ()ve minus V subscript (+)ve divided by 2V subscript 0 times delta y) always have to reflect price changes in response to “equal” increases and decreases in YTM? Why is it I cannot find price change due to 50 bp increase and 20 bp decreases?

Because you are doing the “secant approximation to the tangent” thing where you are getting the slope of the secant line and saying the secant is roughly parallel to the tangent. The situation in which yours is closer to parallel is a very unusual curve and you would have to know something more about the curve than you usually would to make such a statement.

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