스마일은 델타헤징에 유용한가?

Previous researches on the usefulness of the sophisticated and complicated models for pricing and hedging options have showed that unlike in-sample pricing and out-of-sample pricing, there was no clear advantage to incorporating volatility smiles for delta hedging. The possible causes of these results may be related to time-series reliability of the implied parameter estimates. Actually, in this paper, we find that delta hedging errors of less parsimonious models are more affected by past stock returns. So, to examine whether the delta hedging performance can be improved by taking into account the volatility smile implied in the KOSPI 200 index options market prices, we focus on the delta hedging usefulness of the methods which can make a rather simple adjustment of the Black and Scholes’s delta; Vähämaa(2004)'s smile-adjusted delta(SAV), Bates (2005)'s model-free method(SAB), ad-hoc Black and Scholes model(AHBS). As benchmark models, we also investigate hedging performance of two-lognormal mixture model(TLM) which can provide an exact solution with intuitive appeal using weighted sums of Black and Scholes solutions, along with Black and Scholes(1973) model(BS). Our empirical investigation leads to the following overall conclusions. The regression-based approach of the volatility function in which the implicit volatilities are regressed on the strike price and strike price squared is more useful than the method using two-lognormal mixture distribution to reflect the volatility smile for delta hedging. The relative hedging performance across the models using regression-based approach depend on option’s moneyness and hedging horizons. Specifically, in case of (deep) out-of-the money put options, Bates’s model outperforms the other model. In terms of at(near)-the money call/put options and (deep) out-of-the money call options, whether volatility smile should be reflected for delta hedging are affected by hedging horizons. For one-day hedging period, ad-hoc Black Scholes procedure which use directly the regression-based estimate of the volatility function using implicit volatilities shows the best performance because this ad hoc approach amounts to a sophisticated interpolation tool in which implied volatilities are very simply smoothed across strike. But, for the longer hedging horizons, hedge ratios determined by the Black Scholes model appear more reliable than those obtained from the other models. Also, This reliability is distinguished clearly during periods of market turmoil.