Modeling and forecasting implied volatility indices and the application in risk management and option trading

Abstract

Implied volatility, derived from the market price of a market traded derivative, has attracted much attention in recent years, largely motivated by its importance in financial markets. Implied volatility index is a standardized implied volatility that generalized from the corresponding stock index and makes implied volatility available to public investors. This research focuses on modeling and forecasting volatility indices and its application in option trading and risk quantification. Implied volatility index is often regarded as the "investor fear gauge" (Whaley 2009) because its level indicates how much market participants are willing to pay, in terms of implied volatility, to hedge stock portfolios with corresponding stock market index put options or to be long (with limited downside risk) by buying the corresponding stock market index call options. For this reason, academics are interested in the relationship between implied volatility and underlying stock market returns as well as the future realized volatility of the underlying stock market. The Hong Kong market is an emerging market among the global financial markets and volatility index of the Hang Seng Index (HSI) was just published in 2011. The research on VHSI and HSI, VHSI and the future realized volatility of HSI will supplement the study of volatility indices all over the world. Besides, the different nature of fluctuations in Hong Kong market will provide new insights to professional traders. The question whether the dynamics of implied volatility per se can be forecast is of paramount importance to both academics and practitioners. Given that implied volatility is a reparameterization of price of market trading options, this question falls within the vast literature on the predictability of asset prices. In addition, implied volatility is often used as a measure of the market risk and hence it can be used in many asset pricing models. Therefore, understanding whether the variation in implied volatility is predictable can help us understand how expected returns change over time (Corrado and Miller Jr 2006). From a practitioner's viewpoint, if market participants can predict implied volatility changes, they can possibly form profitable option trading strategies. This also has implications for the efficiency of the option markets. One part of this research investigates this question by employing VHSI and some other impacting variables, besides conducting a trading simulation to illustrate the utility of forecasting volatility indices. With the globalization of capital markets, empirical distributions of asset returns have become more and more complicated. Since the underlying index options market has deep and active trading across a broad range of exercise prices, co-movements of volatility indices in different countries need to be examined further (2009). Siriopoulos and Fassas (2009) found there were about thirty public volatility indices in the world. However, extant literature has shed little light on how the volatility indices interact with each other and whether the co-movement of volatility indices can benefit forecasting. Conducting a factor model in VAR form, the co-movement of various volatility indices was examined together with a forecasting performance evaluation, impulse response analysis and variance decomposition. The structure of this dissertation is as follow. The first two chapters present an overview of the implied volatility index and previous researches on implied volatility and implied volatility indices. Research motivation is also explained in the first chapter. In the third chapter we explore the relationship between Hang Seng Index Volatility (VHSI) changes and Hang Seng Index returns, VHSI and future realized volatility of HSI dynamically, with Kalman filter. Also, application of VHSI in risk quantification is investigated in this chapter. Chapter 4 probes whether volatility index can be forecast univariately with ARIMA as well as HAR and ARFIMA, to examine the long-term memory of HSI. The last part of this chapter is involved with an option trading simulation to compare these three models. Chapter 5 presents a Vector Autoregressive (VAR) model combing principal components analysis to explore the co-movement of various volatility indices in the global market associated with the underlying assets returns. The forecasting performances, impulse responses and variance decomposition are examined in this section. Chapter 6 presents a comparative study of volatility modeling and forecasting performance of the GARCH class models, exponential smoothing, historical volatility and random walk for the VHSI and VIX. An option pricing based on the Heston model with the forecasting data is examined to prove the practical significance of this research. This empirical research is also meaningful for hedging with volatility indices derivatives as it highlights modeling and forecasting of volatility indices. Chapter 7 concludes this study and proposes future research directions.

Date of Award	15 Jul 2013
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Kin Keung LAI (Supervisor)