Optimal Dynamic Hedging of Equity Options: Residual-Risks, Transaction-Costs, & Conditioning

85 Pages Posted: 1 Jan 2010 Last revised: 13 Apr 2010

See all articles by Andrea Petrelli

Andrea Petrelli

Credit Suisse Securities

Ram Balachandran

affiliation not provided to SSRN

Olivia Siu

affiliation not provided to SSRN

Rupak Chatterjee

Stevens Institute of Technology

Zhang Jun

affiliation not provided to SSRN

Vivek Kapoor

affiliation not provided to SSRN

Date Written: April 2010

Abstract

Attempted dynamic replication based valuation of equity options is analyzed using the Optimal Hedge Monte-Carlo (OHMC) method. Detailed here are (1) the option hedging strategy and its costs; (2) irreducible hedging errors associated with realistically fat-tailed & asymmetric return distributions; (3) impact of transaction costs on hedging costs and hedge-performance; (4) impact of conditioning hedging strategy on realized volatility. The asset returns are addressed by the General Auto-Regressive Asset Model (GARAM, Wang et al [2009]) that employs two stochastic processes to model the return magnitude and sign and results in a realistic term-structure of the fat-tails, dynamic-asymmetry, and clustering of volatility. The relationship between the option price and ensuing return versus risk characteristics of the option seller-hedger & buyer-hedger are described for different conditioning regimes in GARAM. A hurdle return is employed to assess bounding values of options that reflect hedging costs, the inevitable hedge slippage, & transaction costs. The hurdle return can also be used to make relative-value inferences (e.g., by comparing to the return-risk profile of a delta-1 position in the underlying) or even fit option values to market while still informing the trader about residual risk and its asymmetry between option buyer-hedger and seller-hedger. Tail-risk measures are shown to diminish by conditioning the hedging strategy and valuation on realized volatility. The role of fat-tails and uncertainty of realized volatility and its temporal persistence in controlling the optimal hedge ratios, irreducible hedging errors, and option-trading risk premiums are delineated.

Keywords: options, hedging, kurtosis, skewness, residual-risk, transaction-costs, hurdle-return, risk-capital, volatility trading

JEL Classification: G13, G11, D81

Suggested Citation

Petrelli, Andrea and Balachandran, Ram and Siu, Olivia and Chatterjee, Rupak and Jun, Zhang and Kapoor, Vivek, Optimal Dynamic Hedging of Equity Options: Residual-Risks, Transaction-Costs, & Conditioning (April 2010). Available at SSRN: https://ssrn.com/abstract=1530046 or http://dx.doi.org/10.2139/ssrn.1530046

Andrea Petrelli

Credit Suisse Securities ( email )

One Cabot Square
London, E14 4QJ
United Kingdom

Ram Balachandran

affiliation not provided to SSRN

Olivia Siu

affiliation not provided to SSRN ( email )

Rupak Chatterjee

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Zhang Jun

affiliation not provided to SSRN ( email )

Vivek Kapoor (Contact Author)

affiliation not provided to SSRN ( email )

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