Purpose -The purpose of this paper is to derive an easy-to-implement and highly accurate formula to approximate the change in the bond price resulting from a change in interest rates. Design/methodology/approach -The bond price is raised to an infinitesimal power and the Taylor series expansion is applied. Then, using the well-known modified duration and convexity, the new formula is obtained as a limiting case. Findings -It is proved mathematically and illustrated by numerical examples that the new formula generates better results than both the traditional duration-convexity and the exponential duration approximation formulas. Originality/value -The new formula derived in this paper will be used by risk managers to perform stress-testing on bond portfolios.
This note proposes a new approach of valuing deep in-the-money fixed strike and discretely monitoring arithmetic Asian options. This new approach prices Asian options whose underlying asset price evolves according to the exponential of a Lévy process as a weighted sum of European options. Numerical results from experimenting on three different types of Lévy processes-a diffusion process, a jump diffusion process, and a pure jump process-illustrate the accuracy of the approach.
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