Empirical comparison of alternative stochastic volatility option pricing models: Evidence from Korean KOSPI 200 index options market

Abstract

This article investigates the improvement in the pricing of Korean KOSPI 200 index options when stochastic volatility is taken into account. We compare empirical performances of four classes of stochastic volatility option pricing models: (1) the ad hoc Black and Scholes procedure that fits the implied volatility surface, (2) Heston and Nandi's [Rev. Financ. Stud. 13 (2000) 585] GARCH type model, (3) Madan et al.'s [Eur. Financ. Rev. 2 (1998) 79] variance gamma model, and (4) Heston's [Rev. Financ. Stud. 6 (1993) 327] continuous-time stochastic volatility model. We find that Heston's model outperforms the other models in terms of effectiveness for in-sample pricing, out-of-sample pricing and hedging. Looking at valuation errors by moneyness, pricing and hedging errors are highest for out-of-the-money options, and decrease as we move to in-the-money options in all models. The stochastic volatility models cannot mitigate the “volatility smiles” effects found in cross-sectional options data, but can reduce the effects better than the Black and Scholes model. Heston and Nandi's model shows the worst performance, but the performance of the Black and Scholes model is not too far behind the stochastic volatility option pricing model.