Simple Robust Hedging with Nearby Contracts
57 Pages Posted: 19 Mar 2011
Date Written: March 15, 2011
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: Suggested Citation