Rational Greeks
The IUP Journal of Financial Risk Management, 2016
24 Pages Posted: 4 Jul 2009 Last revised: 13 Mar 2017
There are 2 versions of this paper
Rational Greeks
Rational Greeks
Date Written: August 5, 2016
Abstract
Risk analyses often require the revaluation of complex financial instruments over a large set of risk factor scenarios. In many instances, full revaluation is numerically intensive and hence too costly. In that case one can resort to partial revaluations using Greeks: partial derivatives of the instrument with respect to the underlying value drivers. Taylor series approximations to pricing functions are only valid for relatively small changes in the risk factors and show large approximation errors in the tails of the distribution. In this paper, we show how partial revaluation can be improved by using (modified) Padé rational approximants. Firstly, we show how rational approximation enhances the estimation of effective Greeks from perturbated risk factors. Secondly, we show that rational approximants outperform conventional Taylor approximants in approximating pricing functions. “Rational Greeks” signify a substantial improvement in approximation accuracy, even for substantial changes in risk factors.
Keywords: approximation methods, Padé rational approximants, risk analysis, derivatives, Greeks
JEL Classification: C13, C15, C63
Suggested Citation: Suggested Citation