Parametric models and non-parametric machine learning models for predicting option prices: Empirical comparison study over KOSPI 200 Index options Hyejin Park a , Namhyoung Kim b,⇑ , Jaewook Lee c a Department of Industrial and Management Engineering, Pohang University of Science and Technology (POSTECH), San 31 Hyoja, Pohang 790-784, South Korea b Department of Applied Statistics, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do 461-701, South Korea c Department of Industrial Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744, South Korea article info Keywords: Option pricing Gaussian processes Support vector machines Artificial neural network Black–Scholes model Heston model Merton model abstract We investigated the performance of parametric and non-parametric methods concerning the in-sample pricing and out-of-sample prediction performances of index options. Comparisons were performed on the KOSPI 200 Index options from January 2001 to December 2010. To verify the statistical differences between the compared methods, we tested the following null hypothesis: two series of forecasting errors have the same mean-squared value. The experimental study reveals that non-parametric methods significantly outperform parametric methods on both in-sample pricing and out-of-sample pricing. The outperforming non-parametric method is statistically different from the other models, and significantly different from the parametric models. The Gaussian process model delivers the most outstanding performance in forecasting, and also provides the predictive distribution of option prices. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Despite the recent global financial crisis, options are still one of the most important financial instruments in risk management. The recent surge in option trading volume demonstrates that options are crucial means to hedge against risk. To hedge risks using options, an investor must be aware of the fair price of the option when buy or sell. Option pricing initiated by the Black–Scholes model suffers from several unrealistic assumptions that conflict with the characteristics of option data traded in the real market. For example, the key assumption that the return of stock prices follows a geometric Brownian motion with constant drift and volatility is wrong. The implied volatility from the real market exhibits a ‘‘volatility-smile’’ pattern with different values depend- ing on the time-to-maturity and strike prices. Thus, other advanced alternative parametric models were developed. These models are generally divided into two classes, namely, parametric and non-parametric. Researchers have developed parametric models that can explain the volatility smile in the market data under no-arbitrage conditions. One widely used alternative parametric model is the stochastic volatility model, which assumes that volatility follows a random diffusion process (Heston, 1993). Another widely used model is the jump-diffusion model (Merton, 1976), wherein the movement of underlying assets follows a stochastic process with jumps to Brownian motion. Since the 1990s, other advanced mod- els have been studied actively including more generalized version of Lévy models (Carr, Gaman, Madan, & Yor, 2003; Madan, Carr, & Chang, 1998). Along with the development of IT technology, non-parametric models based on machine learning techniques have been devel- oped to determine the option prices of real market data. Neural network (NN) models have been used to initiate these attempts, and have been extensively discussed in option pricing. Researchers have investigated a variety of non-parametric methodologies for option pricing, since Hutchinson, Lo, and Poggio (1994) demon- strated that NN models obtain a positive result compared with the performance of out-of-sample pricing and delta-hedging (Amilon, 2003; Gencay & Qi, 2001; Gradojevic, Gencay, & Kukolj, 2009; Han & Lee, 2008; Lajbcygier & Connor, 1997; Liang, Zhang, Xiao, & Chen, 2009; Park & Lee, 2012; Yang & Lee, 2011). Most researchers argued that prediction accuracy is improved with con- stant historical volatility compared with that of the Black–Scholes model. This paper investigated the efficiencies of non-parametric machine learning techniques on financial option pricing compared with parametric methods. This study is not limited to traditional http://dx.doi.org/10.1016/j.eswa.2014.01.032 0957-4174/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: nhkim@gachon.ac.kr (N. Kim). Expert Systems with Applications 41 (2014) 5227–5237 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa