Nonparametric option pricing models with empirical analysis in KOSPI option market

Abstract

In this paper, Nonparametric option pricing is studied with empirical data of KOSPI market. So called canonical valuation model (CV1) is implemented with KOSPI200 index data to price the options. In CV1, predictive time-to-expiration index returns are sampled from overlapping historical data and this empirical probability distribution has been transformed to risk-neutral probability distribution by minimizing Kullback-Liebler information criterion (KLIC) distance. To overcome the unpleasant overlapping data property, another nonparametric approach(CV2) is adopted which uses bootstrapping method to sample predictive returns. For comparison purpose, classical Black-Scholes model with historical volatility is also implemented. From the pricing error performance analysis, it has been verified that distribution transformation by minimizing KLIC distance works well. Moreover, despite relative poor performance of predictive return sampling from overlapping data, bootstrapping method showed better pricing performance.