On Stock Market Dynamics and Options Pricing Based on Garch and Regime Switching Models

Abstract

The understanding of the linkage between stock returns, volatility and trading volume is paramount since it provides insights into the financial markets’ micro-structure. The available literature reveals insufficient studies into modeling this correlation and most empirical studies have largely focused on developed markets than on emerging markets. GARCH model and its extensions have been utilized to model this relationship and to reproduce stylized features of financial time series. However, the model does not adequately describe the persistence of the financial markets’ volatility. A model that can permit GARCH parameters to shift across regimes according to a Markov chain process is considered the solution to this problem, thus an attempt of this study is to put forward a regime-switching framework for modeling asset returns dynamics. The aim is to probe the dynamic correlation between stock returns, volatility and trade volume of both emerging and developed markets. In addition, the consequence of adding trade volume to the conditional variance equation of GARCH on volatility persistence is investigated. GARCH and regime-switching (RS) models are utilized to explore the link between stock returns, volatility and trade volume. The RS model is able to capture the structural changes in the variance process across regimes and its use extended to pricing European call options. The model is adapted to include GARCH effects and further implemented to pricing European call options. The estimated call options are compared with the corresponding Black-Scholes(B-S)’ model estimates to establish the model with the best fit. The results reveal well-known features such as volatility clustering, heavy tails, leverage effects and a leptokurtic distribution. The developed markets are described with high volatility clustering and persistence compared with the emerging market and the volatility persistence is observed to decrease as the data changes frequency from daily to weekly. Furthermore, the volatility persistence is observed to dwindle after trade volume is included into the conditional variance equation of GARCH model. However, as the data frequency shifts from daily to weekly, mixed results emerge. The stock returns and volatility from the developed markets have a negative correlation, but the correlation in emerging market is positive. In addition, all the stock returns indices are characterized by regime shifts with heterogeneous conditional volatility, volatility clustering and varying responses to past negative returns. Furthermore, the volatility process stays longer in the high volatility regime of the developed markets before switching to regime 2 compared to the duration of stay in the same regime of the emerging markets. Finally, RS-GARCH model presents the best results when fitted to long-dated options data as compared to RS and B-S models whereas B-S model presents the best fit for short-dated options.