Simple Robust Hedging with Nearby Contracts

57 Pages Posted: 19 Mar 2011

See all articles by Liuren Wu

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business

Jingyi Zhu

University of Utah

Multiple version iconThere are 2 versions of this paper

Date Written: March 15, 2011

Abstract

Most existing hedging theories are derived under strong, idealistic assumptions on both the underlying security price dynamics and the trading environments. Practical concerns such as contract availability, transaction cost, and uncertainty regarding the security price dynamics impose severe limitations on the actual application of these theories. This paper proposes a new, simple, and robust hedging theory that overcomes all these limitations. While most existing hedging methods are based on neutralizing risk exposures defined under a pre-specified model, our hedge portfolio is formed based on the affinity of the derivative contracts. Specifically, in hedging a target option, we form hedge portfolios using three options at three different strikes and two different maturities that form a stable maturity-strike triangle, and we derive the portfolio weights for the hedge portfolio as a function of the strike and maturity spacing of the triangle relative to the target option. Our hedging portfolio does not depend on any assumptions on the underlying risk dynamics, as it is derived purely as a function of the contract characteristics. The portfolio overcomes transaction cost concerns as it only holds three options in static positions. The strikes and maturities of the three hedging options can be flexibly chosen to balance between contract availability, order flow, transaction cost, and hedging effectiveness. Simulation analysis under commonly proposed security price dynamics shows that the hedging performance of our maturity-strike triangles compares favorably against the dynamic delta hedging strategy with daily rebalancing. Although delta hedging performance deteriorates dramatically in the presence of large jumps or stochastic volatility, the hedging performance of our maturity-strike triangles is very stable across different model environments. A historical hedging exercise on S&P 500 index option further highlights the superior performance of our strategies.

Keywords: options, static hedging, forward partial differential equation, local volatility

JEL Classification: E43, E47, G10, G12, C51

Suggested Citation

Wu, Liuren and Zhu, Jingyi, Simple Robust Hedging with Nearby Contracts (March 15, 2011). Available at SSRN: https://ssrn.com/abstract=1787343 or http://dx.doi.org/10.2139/ssrn.1787343

Liuren Wu (Contact Author)

City University of New York, CUNY Baruch College - Zicklin School of Business ( email )

One Bernard Baruch Way
Box B10-247
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)

HOME PAGE: http://faculty.baruch.cuny.edu/lwu/

Jingyi Zhu

University of Utah ( email )

1645 E. Campus Center
Salt Lake City, UT 84112
United States
801 581 3236 (Phone)

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