Rational Greeks

The IUP Journal of Financial Risk Management, 2016

24 Pages Posted: 4 Jul 2009 Last revised: 13 Mar 2017

See all articles by Winfried G. Hallerbach

Winfried G. Hallerbach

Fintelligence CCT; EDHEC Business School - Department of Economics & Finance

Multiple version iconThere are 2 versions of this paper

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

Hallerbach, Winfried George, Rational Greeks (August 5, 2016). The IUP Journal of Financial Risk Management, 2016, Available at SSRN: https://ssrn.com/abstract=1429765 or http://dx.doi.org/10.2139/ssrn.1429765

Winfried George Hallerbach (Contact Author)

Fintelligence CCT ( email )

Salernes, Var 83690
France

EDHEC Business School - Department of Economics & Finance ( email )

France

HOME PAGE: http://https://www.edhec.edu/

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