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

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.