Risk Management for Derivatives in Illiquid Markets: A Simulation Study

20 Pages Posted: 16 Feb 2002

See all articles by Rüdiger Frey

Rüdiger Frey

ETH Zürich

Pierre Patie

Swiss Federal Institute of Technology Zurich (ETH) - Department of Mathematics, RiskLab

Abstract

In this paper we study the hedging of derivatives in illiquid markets. More specifically we consider a model where the implementation of a hedging strategy affects the price of the underlying security. Following earlier work we characterize perfect hedging strategies by a nonlinear version of the Black-Scholes PDE. The core of the paper consists of a simulation study. We present numerical results on the impact of market illiquidity on hedge cost and Greeks of derivatives. We go on and offer a new explanation of the smile pattern of implied volatility related to the lack of market liquidity. Finally we present simulations on the performance of different hedging strategies in illiquid markets.

Keywords: risk management, derivatives, option hedging, volatility, illiquid markets, nonlinear Black-Scholes equation

JEL Classification: G12, G13

Suggested Citation

Frey, Rüdiger and Patie, Pierre, Risk Management for Derivatives in Illiquid Markets: A Simulation Study. Available at SSRN: https://ssrn.com/abstract=300527 or http://dx.doi.org/10.2139/ssrn.300527

Rüdiger Frey (Contact Author)

ETH Zürich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland
0041 1 63 26526 (Phone)
0041 1 63 21085 (Fax)

Pierre Patie

Swiss Federal Institute of Technology Zurich (ETH) - Department of Mathematics, RiskLab ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland
+41 1 632 6820 (Phone)
+41 1 632 1085 (Fax)

HOME PAGE: http://www.math.ethz.ch/~patie/

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