Hedging Market Exposures: Identifying and Managing Market Risks (Wiley Finance) by Bychuk Oleg V. & Haughey Brian

Author:Bychuk, Oleg V. & Haughey, Brian [Bychuk, Oleg V.]
Language: eng
Format: epub
Publisher: Wiley
Published: 2011-06-27T21:00:00+00:00

(4.65)

This estimate, however, is almost guaranteed to be very inaccurate. One can show (Press et al., 2002) that if one can compute V with a fractional accuracy of , then equation (4.65) at best has a fractional accuracy of

(4.66)

achieved when the shift has an optimal value of

(4.67)

Here is the so-called curvature scale of V(f), namely, the typical magnitude of shift over which the quadratic term in expansion (4.23) becomes comparable to V(f). The presence of in equation (4.67) appears to lead to a circular argument: One needs a second-order sensitivity () in order to calculate optimally a first-order one. In practice, one can use a “quick and dirty” estimate of , obtained with a reasonable non-optimal argument shift, in the calculation of . In fact, often one can simply set (unless, of course, near ).

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