Empirical Analysis of GARCH Option Pricing Models

Odd Asgeir Skogstad & Andreas Sæther

Student thesis: Master thesis

Abstract

Extensive literature on financial time series returns find evidence that return exhibit statistical characteristics making the Black-Scholes-Merton model for option pricing unable to model observed data with great accuracy. In a response to the stylized fact that financial return volatility is changing over time and show sign of clustering, a new class of option pricing models have been developed. The models builds on the General-Autoregressive-Conditional-Heteroskedacity (GARCH) volatility modeling framework of Bollerslev (1986). This thesis conduct an empirical comparison of several option pricing models where the return follows a discrete GARCH process. We employ the HN-GARCH model of Heston & Nandi (2000), the NGARCH model of Engle & Ng (1993), the EGARCH model of Nelson (1990) and the GJR-GARCH model of Glosten et al. (1993). Using option data written on the S&P 500 Index from 2014 to 2016 we test the range of GARCH in terms of pricing errors, ability to replicate the volatility smile and significant biases through regression. The models are set up against the Black-Scholes-Merton model, serving as a benchmark. We obtain the model parameters through maximum likelihood on historical time series of return and through minimizing the mean-squared-error (MSE) on a cross sectional data-set of option prices. Our analysis find evidence that the cross sectional approach manages to produce substantially less pricing errors across all models. Measuring the relative performance of the models through MAE, MAPE, RMSE, %RMSE and IVRMSE we find evidence that the HN-GARCH display the least pricing errors in both an in-sample and an out-of-sample analysis. The NGARCH and EGARCH display slightly higher absolute pricing errors overall and show similar characteristics both in- and out-of sample. The GJRGARCH is outperformed over both moneyness and maturity, and demonstrate larger residuals as well as variability in the pricing, especially out-of-sample. While all models manage to replicate the volatility smile characteristics, we present evidence implying that the HN-GARCH is the preferred model to replicate the observed smile. Furthermore, we confirm the relation between pricing errors, time to maturity and moneyness though a regression over MAPE, on a 1% significance level. In accordance with the voluminous existing literature this analysis confirms the GARCH-models relevance within the option pricing theory.

EducationsMSc in Finance and Investments, (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2017
Number of pages137