Abstract

Hedging bond positions under the assumption of a parallel shift of the interest rate curve is well-known and used for a long date in finance. The approximation duration-convexity introduced by L. Fisher and R. Weil is the corresponding main tool. However this last is inaccurately formulated since: the time-passage is neglected, the shift size is assumed to be infinitesimal and the error approximation is out of the control. Our main purpose here is to present how to enhance this classical approximation such that these simultaneous inconveniences may be overcome. Not only our modified approximation leads to a perfect fit of the bond change, but a shift of any arbitrary size is also allowed and a deterministic and explicit estimates of the approximation error becomes available. Though the parallel shift of the interest rate curve is a strong and unrealistic assumption, it remains a standard reference among practitioners and academics. The analysis performed here finds a valuable implication in stress-testing, hedging and managing interest rate risks under more realistic models.

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