Summary
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.
Research of the second author was supported by Credit Suisse Group, Swiss Re and UBS AG through RiskLab, Switzerland and by the Swiss Banking Institute, University of Zurich.
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References
Avellaneda, M., A. Levy, and A. Paras (1995): “Pricing and Hedging Derivative Securities in Markets with Uncertain Volatilities,” Applied Mathematical Finance, 2, 73–88.
Bakshi, G., C. Cao, and Z. Chen (1997): “Empirical Performance of Alternative Option Pricing Models,” Journal of Finance, 52, 2003–2049.
Baum, D. (2001): “Realisierbarer Portfoliowert in illiquiden Finanzmärkten,” Ph.D. thesis, Department of mathematics, Humboldt-Universität Berlin.
Donaldson, R., and H. Uhlig (1993): “The impact of large portfolio insurers on asset prices,” Journal of Finance, 48, 1943–1955.
El Karoui, N., M. Jeanblanc-Picqué, and S. Shreve (1998): “Robustness of the Black and Scholes Formula,” Mathematical Finance, 8, 93–126.
Embrechts, P., R. Frey, and H. Furrer (2001): “Stochastic Processes in Insurance and Finance,” in Handbook of Statistics, ed. by D. Shanbag, and C. Rao, vol. 19, pp. 365–412. North Holland.
Frey, R. (1998): “Perfect Option Replication for a Large Trader,” Finance and Stochastics, 2, 115–148.
Frey, R. (2000): “Market Illiquidity as a Source of Model Risk in Dynamic Hedging,” in Model Risk, ed. by R. Gibson, pp. 125–136. Risk Publications, London.
Frey, R., and P. Patie (2001): “Risk management for derivatives with market illiquidities,” Discussion paper, RiskLab, Department of Mathematics, ETH Zürich, in preparation.
Frey, R., and A. Stremme (1997): “Market Volatility and Feedback Effects from Dynamic Hedging,” Mathematical Finance, 7 (4), 351–374.
Grossman, S., and Z. Zhou (1996): “Equilibrium Analysis of Portfolio Insurance,” Journal of Finance, 51 (4), 1379–1403.
Holthausen, R. W., and R. Leftwich (1987): “The Effect of Large Block Transactions on Security Prices — A Cross-Sectional Analysis,” Journal of Financial Economics, 19, 237–267.
Jarrow, R. (1994): “Derivative Securities Markets, Market Manipulation and Option Pricing Theory,” Journal of Financial and Quantitative Analysis, 29, 241–261.
Kampovsky, A., and S. Trautmann (2000): “Price impact of Xetra-traders,” Preprint, Department of Economics, University of Mainz.
Kloeden, P., and E. Platen (1992): Numerical Solution of Stochastic Differential Equations, Applications of Mathematics. Springer, Berlin.
Lyons, T. (1995): “Uncertain Volatility and the Risk-free Synthesis of Derivatives,” Applied Mathematical Finance, 2, 117–133.
Platen, E., and M. Schweizer (1998): “On feedback effects from hedging derivatives,” Mathematical Finance, 8, 67–84.
Rubinstein, M. (1985): “Nonparametric Tests of Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 to August 31, 1978,” Journal of Finance, 40, 455–480.
Schönbucher, P., and P. Wilmott (2000): “The feedback-effect of hedging in illiquid markets,” SIAM Journal of Applied Mathematics, 61, 232–272.
Sircar, R., and G. Papanicolaou (1998): “General Black-Scholes Models Accounting for Increased Market Volatility from Hedging Strategies,” Applied Mathematical Finance, 5, 45–82.
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Frey, R., Patie, P. (2002). Risk Management for Derivatives in Illiquid Markets: A Simulation Study. In: Sandmann, K., Schönbucher, P.J. (eds) Advances in Finance and Stochastics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04790-3_8
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DOI: https://doi.org/10.1007/978-3-662-04790-3_8
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