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 con- sidered 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 mar- kets 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 mar- kets 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 pro- cess 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.
TABLE OF CONTENTS
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
TABLE OF CONTENTS vi
LIST OF TABLES viii
LIST OF FIGURES x
LIST OF ACRONYMS AND ABBREVIATIONS xi
CHAPTER 1: INTRODUCTION
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Statement of the problem . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Objectives of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Main objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Specific objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Scope of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Significance of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
CHAPTER 2: LITERATURE REVIEW
CHAPTER 3: METHODOLOGY
3.1 Introduction 16
3.2 A review of stylized facts of returns 16
3.3 Modeling the underlying asset 18
3.4 The ARCH model 18
3.5 The GARCH Model 19
3.5.1 Conditional mean specification 20
3.5.2 Explanatory variables in the conditional variance 20
3.6 The GARCH-M Model 21
3.7 The exponential GARCH (EGARCH) Model 21
3.8 Markov-Switching GARCH (MS-GARCH) Model 22
3.9 Conditional distributions 23
3.9.1 Normal distribution 23
3.9.2 Student-t distribution 24
3.9.3 The generalized error distribution(GED) 25
3.10 Estimation of model parameters 25
3.10.1 The ARCH model parameter estimation 25
3.10.2 The GARCH model parameter estimation 26
3.10.3 MS-GARCH model parameter estimation 28
3.11 Option pricing 28
3.11.1 Regime switching market dynamics 29
3.11.2 Risk-neutral measure 30
3.11.3 Derivation of the Black-Scholes formula by change of measure 32
3.11.4 Regime-switching (RS) model 34
3.11.5 The RS model parameter estimation 41
3.11.6 Regime switching-GARCH (RS-GARCH) model 43
3.11.7 RS-GARCH model parameter estimation 44
3.12 Statistical tests 45
3.12.1 Augmented Dickey-Fuller (ADF) test 45
3.12.2 Jarque-Bera(JB) Test 45
3.12.3 Ljung Box 46
3.12.4 Lagrange Multiplier (LM) test 46
3.12.5 Root Mean Square Error (RMSE) 47
CHAPTER 4: RESULTS AND DISCUSSION
4.1 Empirical data 48
4.2 Descriptive statistics 48
4.3 Empirical findings and discussion 51
4.4 Option pricing 73
4.4.1 Empirical data 73
4.4.2 Descriptive statistics 73
4.4.3 Empirical findings and discussion 74
CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions 81
5.2 Recommendations 85
REFERENCES 86
Appendix A List of published/Unpublished papers as part of this study 93
Appendix B Some R codes used in data analysis 94
List of Tables
4.1 Basic statistics for daily FTSE100, S&P500 and NSE20 stock prices 48
4.2 Basic statistics for daily RUT, FB and GooG stock prices 49
4.3 Descriptive statistics for index returns and log volume 49
4.4 Statistical tests for the indices returns and log volume 55
4.5 The parameter estimates of GARCH(1,1) model for daily indices returns 58
4.6 The parameter estimates of GARCH(1,1) model for weekly indices returns 58
4.7 The parameter estimates of GARCH-M(1,1) model for daily indices returns 59
4.8 The parameter estimates of GARCH-M(1,1) model for weekly index returns 60
4.9 The parameter estimates of EGARCH(1,1) model for daily indices returns 61
4.10 The parameter estimates of EGARCH(1,1) model for weekly index returns 61
4.11 The parameter estimates of MS-GARCH(1,1) model for daily indices returns 63
4.12 The parameter estimates of MS-GARCH(1,1) model for weekly index returns 63
4.13 The parameter estimates of MS-EGARCH(1,1)model for daily indices returns 65
4.14 The parameter estimates of MS-EGARCH(1,1) model for weekly index returns 65
4.15 GARCH(1,1) parameter estimates for daily indices returns with trading volume 66
4.16 GARCH(1,1) estimates for weekly index returns with volume 67
4.17 GARCH-M(1,1) estimates for daily indices returns with volume 68
4.18 GARCH-M(1,1) estimates for weekly indices returns with volume 68
4.19 EGARCH(1,1) estimates for daily indices returns with volume 69
4.20 EGARCH(1,1) estimates for weekly indices returns with volume 70
4.21 Regime switching model estimates for the returns-volume relationship 71
4.22 Regime switching estimates for indices returns 72
4.23 Correlation coefficients for returns and trading volume 73
4.24 Basic statistics for RUT, FB and GooG indices returns 74
4.25 Correlation coefficients for RUT,FB and GooG 74
4.26 Regime-switching(RS) model parameter estimates 76
4.27 RS-GARCH model parameter estimates 77
4.28 The Call Option prices 79
4.29 RMSE for the Black-Scholes, Regime-switching and RS-GARCH models 79
List of Figures
1 Empirical density versus normal distribution, and qq-plots for daily returns 50
2 Empirical density versus normal distribution, and qq-plots for daily log volume 50
3 Empirical density versus normal distribution, and qq-plots for weekly returns 51
4 Empirical density versus normal distribution, and qq-plots for weekly log volume 51
5 The daily stock indices and stock returns 52
6 The daily trading volume and log volume 52
7 The weekly stock indices and stock returns 53
8 The weekly trading volume and log volume 53
9 Daily absolute returns and log volume 53
10 Weekly absolute returns and log volume 54
11 Daily square returns and log volume 54
12 Weekly square returns and log volume 54
13 ACF for the daily returns and log volume 55
14 ACF for the weekly returns and log volume 56
15 ACF for the daily absolute returns and log volume 56
16 ACF for the weekly absolute returns and log volume 56
17 ACF for the daily square returns and log volume 56
18 ACF for the weekly square returns and log volume 57
19 Stock prices and stock returns 75
20 Smoothed probabilities for Russell 2000 index 75
21 Smoothed probabilities for Facebook index 76
22 Smoothed probabilities for Google index 76
23 25 days call option prices 78
24 258 days call option prices 78
LIST OF ABBREVIATIONS AND ACRONYMS
ADF Argumented Dickey-Fuller
AR Autoregressive
ARMA Autoregressive Moving average
ARCH Autoregressive Conditional Heteroscedasticity
BS Black Scholes
EGARCH Exponential Generalized Autoregressive Conditional Heteroscedasticity
FTSE Financial Times Stock Exchange
GARCH Generalized Autoregressive Conditional Heteroscedasticity
GBM Geometric brownian motion
GED Generalized Error Distribution
LM Lagrange Multiplier
MDS Martingale Difference Sequence
MLE Maximum Likelihood Estimate
MS-GARCH Markov switching Generalized Autoregressive Conditional Heteroscedasticity
NIG Normal Inverse Gaussian
NSE Nairobi Securities Exchange
SDE Stochastic differential equation
S&P500 Standard and Poor Index
RS Regime Switching
RS-GARCH Regime Switching Generalized Autoregressive Conditional Heteroscedasticity
CHAPTER 1
INTRODUCTION
1.1 Background
The existing studies on financial modeling unveil that the connection between returns from stocks, volatility and the total traded shares have been broadly investigated in both established and developing stock markets. The understanding of this connection is paramount because it gives investors the insight of the financial market micro-structure. Abbondante et al. (2010) defines volatility as a sta- tistical measure of asset returns dispersion, and refers to the total shares transacted within a specific period of time as trading volume(or volume). According to him, volatility may be calculated by deter- mining the variance or standard deviation of an asset return and that a higher value is an indication of investment returns that are highly dispersed and this can be associated with a higher risk. Arguably, the success of stock market heavily relies on volatility in the sense that when the volatility reduces, the stock price may go up and vice versa. In other words, this implies that when volatility increases, market risk rises as well, and returns may fall. Moreover, Abbondante et al. (2010) contends that trading volume can be employed in technical analysis as an indicator of the direction of the stock price. Trading volume gives investors an estimate of the stock market value and to some extent it can confirm trend or trend reversal and it is likely that as trade volume increases, the stock prices gener- ally would move in a similar direction. It is thus worth noting that a thorough understanding of how stock returns, volatility and volume are related is essential. According to Wiley and Daigler (1999), information flow into the market play a crucial role in determining the stock price and volume rela- tionship, whereas, Karpoff (1987) on the other hand, argue that price-volume empirical relationship is paramount because of the fact that it gives insights into the understanding of the many theories that compete to widely spread ideas about the role played by the information that flows into the market. The investors’ motivation to trade is mostly determined by their trading objective; it could be to spec- ulate on market information or portfolios diversification to spread the risk, or the desire for liquidity. These varied trading motives stem from the interpretation of various data sources. As a consequence, trading volume may come from any of the investors with various information sets. Many empirical studies disclose that information flow into the market is linked to volatility and trading volume, as shown by the studies of Gallant et al. (1992), Lamoureux and Lastrapes (1990), and He and Wang (1995). All these studies, reports that the arrival of new information into the market causes changes in stock prices and as a consequence the returns on stock, volatility and trade volume are positively associated.
Moreover, investors are motivated by larger returns to investment and this results in capital flow, however, it is not easy to forecast returns in a volatile market environment, see Attari et al. (2012). According to Attari et al. (2012) and Glascock and Hsieh (2014), emerging stock markets are associated with extremely volatile stock returns emanating from the stock market having low volume. A market at the development stage of becoming a mature and developed system where growth is steady and political risks (the risk that an investment is likely to be adversely affected by political changes and instability in a country) are low, is known as an emerging market. These markets are in most cases located in undeveloped countries that are striving to achieve a steady business infrastructure. An investment in an emerging market has the tendency to be volatile and uncertain, and investors demand higher potential returns in exchange for the higher risk. In general, emerging markets are characterized by low income, rapid growth, high volatility currency swings, and high potential re- turns. Note that, an emerging market becomes a developed market if it has all the traits of a developed market. On the other hand, a developed market is a country that is most developed in terms of its economy and capital markets. That is, it is an economy (country) with a high level of economic ac- tivity characterized by high per capita income or per capita gross domestic product (GDP), high level of industrialization, developed infrastructure, technological advancement, and a relatively high rank in human development, health and education. In a developed market there are high levels of liquid- ity in debt and equity, political and financial stability (hence less risk), high economic development, and the market is open to foreign investment and this provides accessibility to global investors and hence encourages a higher volume of investment and transactions. In general, a developed market economy is characterized by high income, high human development rank, service sector domination, technological, and high level of infrastructure development.
A study by Girard and Biswas (2007) compared stock returns’ volatility and trade volume in both established and developing markets and reported a negative relationship between the two markets. Ac- cording to Al Samman and Al-Jafari (2015) trading volume is a crucial indicator that can be utilized to gauge the market strength because it includes information about the stock market’s performance. Empirical studies have looked at the dynamic and contemporaneous correlation between returns from stocks and trading volume. In this regard, Lee and Rui (2000) report that in developed markets volume is granger-caused by returns and similarly, Mahajan and Singh (2009) unveils that volatility and volume are positively correlated in addition to disclosing that returns granger-cause trading volume (one-way causality). Furthermore, studies by Christie (1982) disclose that volatility and trading volume are negatively correlated while Rogalski (1978) on the other hand established a positive contemporaneous link between volume and absolute returns by utilizing month-on-month data. Recently, Jiranyakul (2016) investigated the dynamic association between returns on stocks, volatility and trade volume from the Thai Stock exchange and established that trade volume is paramount in dynamic relationships. Pertaining to the subprime mortgage crisis in the United States, the trade volume creates both returns and volatility. Moreover, the available literature reports a contemporaneous association between volatility and trade volume from the Thai Stock market. Despite this remarkable empirical and theoretical investigations on stock returns, volatility and trading volume correlations, blended results have been established in general. In addition, the focus of majority of these studies have been on the established stock markets rather than emerging stock markets which leave inadequate similar literature for emerging markets.
Lamoureux and Lastrapes (1990) in their study claim that the random arrival of information into the market causes price movements and consequently this leads to trade volume fluctuations. Despite information flow being unobserved, trade volume can be utilized as an exogenous variable for return series heteroscedasticity of variability of return series in question. When trade volume is factored into GARCH model, volatility persistence, as reflected by the ARCH and GARCH effects, may be minimized or eliminated. Moreover, Lamoureux and Lastrapes (1990) argue that when trade volume is added into the conditional variance equation, the conditional volatility persistence vanishes. Results similar to that of Lamoureux and Lastrapes (1990) have been established by studies of Miyakoshi (2002) and Omran and McKenzie (2000) who investigated the Australian equities and found that the volatility persistence decreased considerably after trade volume is utilized as a proxy for the information arrival rate. The studies of Huang and Yang (2001), Chen et al. (2001), Yu¨ksel (2002), Salman (2002) and Ahmed et al. (2005) reports contrasting results that volatility persistence does not decrease when trade volume is incorporated into the conditional volatility equation.
Financial markets have been observed quite often to exhibit an abrupt change of their behavior, for instance, previous studies reveals that volatility on stock returns changes with time and the change tend to persist. Moreover, some stylized features of volatility for instance volatility clustering, lever- age effects, higher volatility emanating from non-trading periods, etc, have been reported by many empirical studies. Volatility has been found to be a vital factor that influences option pricing despite the fact that it is a difficult factor to estimate, however, once estimated volatility may be utilized to determine future stock prices or the option prices. Black-Scholes model which is reported from the existing literature to have been broadly utilized in option pricing assumes that volatility is steady until the lapse time, which is not the case since volatility is known to change over time. Also, the model is deemed a single volatility regime model. Furthermore, the conditional variance of returns is time varying and researchers have paid attention to this stylized fact by building models that cap- ture the changing variance, either in a continuous, see Heston (1993), or discrete, see Engle (1982), time setting. Unfortunately, both discrete and continuous time states of nature have given rise to in- completeness, for example, the multiplicity of equivalent martingale measures involves a continuum of equilibrium prices. As a result, the question of choosing the best model arises. For instance, an approach for pricing options was developed by Duan (1995) that considered a GARCH model with Gaussian innovations whereas Heston and Nandi (2000), basing their argument on the methodology by Duan (1995), considered a new conditionally Gaussian model to capture skewness in prices of options. They developed a nearly closed form formulation for pricing call options and used empirical data to verify its pricing performance. However, this model is conditionally Gaussian which means that it does not reflect the behavior of short-term equity options smiles. The model was later extended by Christoffersen et al. (2006) who utilized Inverse Gaussian distribution in order to increase the skewness effect. On the other hand, ARCH - type models have been widely used to model the varying volatility, however, in order to capture the sudden changes of financial market behavior such as the volatility swings, Regime switching models of Hamilton (1989) are utilized. According to an unob- servable process that creates switching among a finite range of regimes, these model parameters as- sume various values in diverse time periods. In support of regime-switching models with autonomous mean and variance changes, Bollen et al. (2000) and Hardy (2001) suggested a regime-switching log-normal (RSLN) model in which log-returns follow a normal distribution with mean and variance that are dependent on the regime variable. To investigate the volatility of the valued-weighted Tai- wan Stock Index returns, Li and Lin (2003) used the Hamilton and Susmel (1994) Markov-Switching ARCH model. Additionally, Markov regime-switching models have been used to show that volatility expectations in the German, Japanese, and US stock markets are regime-specific. Pricing options under regime switching model has been widely suggested, however, pricing of regime risk has been a problem. Regime risk is linked to the changing economic conditions and hence ought to be priced. Furthermore, valuing regime risk in a Markov regime switching model is a subject that is yet to be completely investigated in the literature. In fact, the impact of switching regimes in the underlying asset price dynamics on the behavior of option prices is addressed through direct pricing of regime risk. It also provides some insight into how macroeconomic factors affect option prices, which is particularly significant when pricing a long-maturity option because macroeconomic conditions might vary over time.
In conclusion, despite the fact that extensive research on stock returns, volatility, and trading volume exists, the majority of studies have focused mostly on developed stock markets, leaving analogous research on emerging markets lacking. However, this notwithstanding the documented evidence reveals results that are not in total consensus about the association between returns on stocks, volatility and trade volume. In addition, the issue of including trading volume in GARCH model’s conditional variance equation and as to whether volatility persistence decreases or even vanishes al- together, has been found to disclose conflicting results. Another issue that emerges from the available literature is that the GARCH model and its extensions have been utilized to capture the stylized char- acteristics of financial time series for instance, heavy tails, clustering of volatility, leverage effects, long-memory, leptokurtic distribution, among others. The empirical researches report that stock re- turns volatility poses several issues that GARCH-type models fail to reflect well, see Bauwens et al. (2006). In particular, these models frequently exhibit a high level of conditional volatility persistence. Ardia et al. (2019) demonstrates that the GARCH-type model does not reflect the actual volatility change whenever there is regime changes in volatility dynamics. The volatility change in a market with regime switches can best be captured by considering a regime switching model because it per- mits the GARCH parameters to change over time. As a consequence, this study proposes to utilize GARCH-type and a regime-switching model to model the underlying asset’s dynamics as well as to probe the contemporaneous and dynamic correlation between returns on stock, volatility and trade volume from both emerging and developed markets. This is further utilized to investigate how inte- grating trade volume into the GARCH-type models’ conditional variance equation affects volatility persistence.
Moreover, modeling the underlying asset’s dynamics using a regime switching model is extended to pricing European options and the Blackscholes model is used as a benchmark model for the option pricing. In fact, a regime-switching model for pricing European options is proposed in this paper when the underlying asset dynamics are dependent on market regimes. The formulation of this model is based on a geometric Brownian motion that is guided by a two-state continuous-time Markov chain and by an application of a change of measure, an option price is developed using risk-neutral valuation. The regime switching (RS) model is modified to include GARCH effects and dynamics resulting to regime-switching GARCH model, hereinafter referred to as RS-GARCH. The implementation of these two models is done by computing the European call option prices for some chosen stock market indices and the results compared with those from the famous Black-Scholes model. This comparison is necessary for establishing the best model for pricing the European options.
In general, in this study, the stock markets dynamics are modeled with the aim of probing the relationship that exists between stock returns, volatility and trading. Moreover, the dynamics of the stock returns’ volatility in a regime switching market is investigated and applied in pricing the European options. The principal contributions of this study are that;
• The relationship between stock returns, volatility and trading volume is investigated using both GARCH-type and Regime switching models. A comparison of this relationship for both developed and emerging financial markets is carried out, such a comparative study that uses both GARCH-type and Regime switching models is missing from literature. Moreover, the relationship between asymmetric volatility and trade volume using GARCH-type models is investigated.
• The dynamics of stock returns’ volatility is probed using the GARCH-type and Regime switch- ing models. The GARCH-type models conditional to normal, student-t and GED distributions are utilized for both developed and emerging markets. The regime switching model is applied to the two market data sets to capture the stock market dynamics in a regime switching financial market setting. Moreover, a comparison of the stock market dynamics for the two sets of mod- els is implemented and such a comprehensive comparison has not been carried out by earlier studies.
• The effect of trade volume on volatility asymmetry and volatility persistence when trade vol- ume is added to the conditional variance equation of GARCH-type model is investigated under the three conditional distributions; normal, student-t and GED. The existing literature has not captured the relationship between trade volume and volatility asymmetry, and a comparison of the same for both emerging and developed markets is lacking. This study, therefore, has filled up this gap. Furthermore, this study adds to the existing literature by investigating the effect of trade volume on volatility persistence since earlier studies have reported conflicting results. This notwithstanding, the empirical studies existing in literature have not compared the case for developed and emerging markets in addition to the fact that many of these studies have fo- cused more on modeling developed markets than emerging market. These two issues have been addressed by this study.
• The research by Hardy (2001) assumed that the stock returns are log-normally distributed, and utilized a regime switching model to price European options. In this study, this assumption is dropped and instead the European call options are priced using the regime switching model under the assumption that the returns on stocks follow a normal distribution. Moreover, a large data set with many observations as compared to the two market indices data considered by Hardy (2001) is utilized so as to increase the chance of getting better descriptions of the model in the options pricing. Finally, the regime switching model is adapted to include GARCH effects which results to a Regime switching GARCH (RS-GARCH) model and this model is utilized in pricing the European options. The results of the European call options estimated from both the RS and RS-GARCH models are compared with those of the Black-Scholes model and the model with better fit is determined.
1.2 Statement of the problem
Modeling stock returns is an important task in financial markets and the past couple of years have witnessed an increase in research that are geared towards modeling the financial time series of both emerging and developed stock markets. The majority of empirical studies on the dynamic and con- temporaneous association between returns on stocks, volatility, and trade volume have focused on developed economies such as, the US, UK, Japan, and Hong Kong stock markets, as compared to emerging markets. These prior studies reports a link between returns on stocks, volatility and trade volume, however, some few studies have reported conflicting results pertaining this relationship. Most of these previous empirical studies generally support the mixture of distribution hypothesis (MDH) model in explaining the association between trade volume and stock returns in the setting of informa- tion arrival into the market. Many empirical studies that utilized the MDH model have explained the volatility persistence by adding trading volume in GARCH model as a proxy for information arrival. The existing literature reveals that there are very few studies that have utilized asymmetric GARCH models to investigate the connection between returns and trade volume. On the other hand, financial markets have been observed quite often to exhibit an abrupt change of behavior, for instance, previ- ous studies have shown that stock returns volatility changes with time and the change tend to persist. Regime switching models proposed by Hamilton (1989) are utilized in modeling dynamic switches of the salient characteristics of financial time series, for instance, volatility asymmetry, among others. In the context of modeling the dynamics of the correlation between stock returns and trade volume, it is revealed that Regime switching models have hardly been used by prior studies to model this relationship. This study focuses on modeling the underlying asset returns using GARCH models and its extensions and Regime Switching models as well as applying these models in pricing the European options. Furthermore, the existing literature reveals limited information on whether regime-switching and RS-GARCH models outperform the famous Black-Scholes model in pricing European options. Therefore, a regime switching model for pricing European options is constructed and modified to include GARCH effects and dynamics resulting to regime-switching GARCH model.
1.3 Objectives of the study
1.3.1 Main objective
The overall objective of the study is to model the correlation between stock returns, volatility and trading volume of the emerging and developed financial markets and to price few financial derivatives such as European options.
1.3.2 Specific objectives
(i) To analyze stock returns volatility dynamics in both developed and emerging markets based on GARCH and Regime switching models.
(ii) To investigate the dynamic correlation of stocks returns, volatility and trade volume in emerging and developed financial markets.
(iii) To investigate the asymmetric relationship between trade volume and stock returns using GARCH models.
(iv) To price European options using regime switching and RS-GARCH models.
1.4 Scope of the study
This study probes the dynamic and contemporaneous correlation between stock returns, volatility and total number of shares traded in Nairobi securities exchange (NSE20), S&P500 and FTSE100 market indices. The dynamic structure of the underlying stock returns is modelled using GARCH models and their extensions, Regime switching, and MS-GARCH models conditioned with Gaussian, student-t, and generalized error distributions (GED) specifications. Application of these models is extended to the pricing of European options.
1.5 Significance of the study
Modeling financial market index as well as option pricing is significant in the following manner; first, it provides the understanding of the financial markets micro-structure. Secondly, it demonstrates the rate of information flow to the market, how the information is widely spread and how it influences stock returns by applying different models, for instance the GARCH models specify a symmetric volatility response to news. Finally, the use of exponential GARCH models gives new insight into the asymmetric effects of volatility, trading volume, and their impact on stock returns. The understanding of the dynamic structure of the underlying assets is the basis for application of the knowledge into pricing options.
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