Robust hedging performance and volatility risk in option markets: Application to Standard and Poor's 500 and Taiwan index options

We investigate daily robust hedging performance with trading costs for markets of Standard and Poor's (S&P) 500 Index options (SPX) and Taiwan index options (TXO). In addition, we conduct a theoretical analysis to cope with the price limit constraint in TXO. Robust hedging refers to minimal model dependence on a risky asset price. Two hedging categories, including “Model-Free” and “Volatility-Model-Free,” are investigated, and nonparametric methods for volatility estimation are considered in our empirical study. In particular, instantaneous volatility is estimated by a proposed nonlinear correction scheme of the Fourier transform method (Malliavin & Mancino, 2009), justified by a simulation study for a local volatility model. We found an asymmetric phenomenon in hedging performance. Hedging portfolios constructed from the “Volatility-Model-Free” category were found to induce much higher Sharpe ratios than those from the “Model-Free” category on SPX, while they were found to perform comparably on TXO. Motivated from the price limit regulation in Taiwan, we further develop a time-scale change method to explain this phenomenon. Asymptotic moment estimates of differences in some hedging portfolios are consistent with our empirical findings.