Essays on value at risk and asset price bubbles

Ph.D. ThesisThis thesis describes a series of investigations into the reliability of different financial risk models for measuring downside risks during financial crises caused by the bursting of asset price bubbles. It also provides further insight into modelling asset price series with periodically collapsing asset price bubbles. We start by reviewing the volatility models that are commonly used for quantifying downside financial risks in Chapter 2. The characteristics of several important univariate and multivariate autoregressive conditional heteroscedasticity family volatility models are reviewed. In Chapter 3, we apply the volatility models to identify the direction of volatility spillover effects among stock markets. The financial markets considered in this study include Japan, China, Hong Kong, Germany, the United Kingdom, Spain, the United States, Canada, and Brazil. Findings from both the dynamic conditional correlation (DCC) and asymmetric DCC models show that the asymmetric volatility spillover effect is highly significant among financial markets, while the asymmetric correlation spillover effect is not. Financial contagion will be reflected in price volatility, but not in correlations. Subsequently we move to testing different Value-at-Risk (VaR) approaches using market data. We define 1 June 2008 to 1 June 2009 as the financial crisis period. We study nine hypothetical single-stock portfolios and nine hypothetical multiple-asset portfolios in the nine countries considered. Both the univariate and multivariate VaR approaches are tested and the results show that the long memory RiskMetrics2006 model outperforms all other univariate methods, while the Glosten-Jagannathan-Runkle DCC model performs well among the multivariate VaR models. Next, in Chapter 5 we use simulations to explore the characteristics of financial asset price bubbles. Evans (1991) proposed a model for investigating asset price movements with periodically collapsing explosive bubbles. We modify and extend this model to make it more realistic; as a result the modified model better controls the growth and collapse of bubbles, while exhibiting volatility clustering. In the simulation tests, the RiskMetrics VaR model performs well during financial turmoil. Finally, we discuss the sup-augmented Dickey-Fuller test (SADF) and the generalized SADF test for identifying and date-stamping asset price bubbles in financial time series. Unlike in Chapter 4 (where we use personal judgement to define financial bubble periods), pre- and post-burst periods are defined here based on the identification results of the asset price bubbles’ origination and termination dates from the backward SADF test. Our empirical results show that the criticism that VaR models fail in crisis periods is statistically invalid

Forecasting Volatility and Analyzing the Features of Volatility by three different methods- empirical study based on SSE 50ETF

Abstract China financial capital market has attracted great attention since it was booming fast. Until 2016 (after 26 years the Shanghai Stock Exchange Market was established), the value of Shanghai Stock Exchange Market reached 29463744 billion RMB which roughly equals to 3440532 billion pounds under current exchange rate, which ranks fifth in the world. In 9th February 2015, the first option in China financial capital market, which is SSE 50ETF option, has been official listed on the Shanghai Stock Exchange. It means that Chinese financial capital market had developed into more marketization. It is necessary to describe how the volatility will change in the future time point through to analysis the changes of the historic volatility or information of options contracts, since the volatility is considered as the most significant feature to measure the risks of portfolio. Pan and Poteshman (2008) conclude that the volatility can affect the option prices. French, Schwert, and Stambaugh (1987) also examine the relationship between volatility and stock return. Therefore, volatility is worth to forecast the volatility of stock because it could assist the stock investors to against risk and manage their portfolio more efficient. However, it is hard to forecast the volatility in the stock market, because there are many limitations on different methods. Firstly, volatility is constant, when we use classic Black-Scholes model. However, volatility should change varying time (Dumas, Fleming, and Whaley, 1998). Secondly, different forecasting models are suitable for different terms of volatility. GARCH-type model has better ability of predicting in short term, while implied volatilities are more efficient in the prediction of future volatilities for over 1 month (Koopman, Jungbacker and Hol, 2005). However, stock option volatility includes more information, such as information of option contracts. Pong, Shiuyan, et al (2004) compare three types of models and find that intraday rates have most accurate forecasts in short term, while implied volatility and historical volatility are similar in long term predicting. As the representative of emerging market, the financial capital market in China is unique but imperfect, it is hard to apply some popular forecasting methods to this market without analyzing (Yang, Yang and Zhou, 2012). Thus, this dissertation is trying to analysis which forecasting method of three will provide better performance in China stock market. This dissertation collects the data of daily price of SSE 50ETF from WIND database. We find the forecasting value of historical volatility (collected from daily return), realized volatility (the sum of squared intraday return) and implied volatility (collected from option contracts). Firstly, we applied GARCH model and EGARCH model to analysis the leptokurtosis and fat-tail, volatility clustering and leverage effect of SSE 50ETF. Because GARCH model is consider as the best way to describe the feature of volatility such as leptokurtosis and fat-tail, volatility clustering, besides that EGARCH model can also test the asymmetry of series. Secondly, we considered long-memory by HAR-RV model for realized volatility, which is regarded as most accurate volatility estimation. Thirdly, we used Black-Scholes model to compute implied volatility and observed volatility smile and term structure of the SSE 50ETF. Compared with three different types of volatility, we found that the features of these volatilities, such as leptokurtosis and fat-tail, volatility clustering, leverage effect and long memory, in the China market. And these three methods both have good ability to predict volatility. Key words: forecasting volatility of options, GARCH-family model, HAR-RV model, Implied Volatility of option

A cluster driven log-volatility factor model: a deepening on the source of the volatility clustering

We introduce a new factor model for log volatilities that performs dimensionality reduction and considers contributions globally through the market, and locally through cluster structure and their interactions. We do not assume a-priori the number of clusters in the data, instead using the Directed Bubble Hierarchical Tree (DBHT) algorithm to fix the number of factors. We use the factor model and a new integrated non parametric proxy to study how volatilities contribute to volatility clustering. Globally, only the market contributes to the volatility clustering. Locally for some clusters, the cluster itself contributes statistically to volatility clustering. This is significantly advantageous over other factor models, since the factors can be chosen statistically, whilst also keeping economically relevant factors. Finally, we show that the log volatility factor model explains a similar amount of memory to a Principal Components Analysis (PCA) factor model and an exploratory factor model

Realized volatility and absolute return volatility: a comparison indicating market risk

Measuring volatility in financial markets is a primary challenge in the theory and practice of risk management and is essential when developing investment strategies. Although the vast literature on the topic describes many different models, two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior, absolute return volatility is easier to calculate and, as a risk indicator, has approximately the same sensitivity as realized volatility. Our detailed empirical analysis yields valuable guidelines for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods.ZZ, ZQ, BL thank "Econophysics and Complex Networks" fund number R-144-000-313-133 from National University of Singapore (www.nus.sg). TT thanks Japan Society for the Promotion of Science Grant (www.jsps.go.jp/english/e-grants/) Number 25330047. HES thanks Defense Threat Reduction Agency (www.dtra.mil) (Grant HDTRA-1-10-1-0014, Grant HDTRA-1-09-1-0035) and National Science Foundation (www.nsf.gov) (Grant CMMI 1125290). ZZ thanks Chinese Academy of Sciences (english.cas.cn) Grant Number Y4FA030A01. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. (R-144-000-313-133 - National University of Singapore; 25330047 - Japan Society for the Promotion of Science Grant; HDTRA-1-10-1-0014 - Defense Threat Reduction Agency; HDTRA-1-09-1-0035 - Defense Threat Reduction Agency; CMMI 1125290 - National Science Foundation; Y4FA030A01 - Chinese Academy of Sciences)Published versio

Tick size and price diffusion

A tick size is the smallest increment of a security price. It is clear that at the shortest time scale on which individual orders are placed the tick size has a major role which affects where limit orders can be placed, the bid-ask spread, etc. This is the realm of market microstructure and there is a vast literature on the role of tick size on market microstructure. However, tick size can also affect price properties at longer time scales, and relatively less is known about the effect of tick size on the statistical properties of prices. The present paper is divided in two parts. In the first we review the effect of tick size change on the market microstructure and the diffusion properties of prices. The second part presents original results obtained by investigating the tick size changes occurring at the New York Stock Exchange (NYSE). We show that tick size change has three effects on price diffusion. First, as already shown in the literature, tick size affects price return distribution at an aggregate time scale. Second, reducing the tick size typically leads to an increase of volatility clustering. We give a possible mechanistic explanation for this effect, but clearly more investigation is needed to understand the origin of this relation. Third, we explicitly show that the ability of the subordination hypothesis in explaining fat tails of returns and volatility clustering is strongly dependent on tick size. While for large tick sizes the subordination hypothesis has significant explanatory power, for small tick sizes we show that subordination is not the main driver of these two important stylized facts of financial market.Comment: To be published in the "Proceedings of Econophys-Kolkata V International Workshop on "Econophysics of Order-driven Markets" March 9-13, 2010, The New Economic Windows series of Springer-Verlag Italia

Emergence of long memory in stock volatility from a modified Mike-Farmer model

The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF model does not show sound long memory. We propose a modified version of the MF model by including a new ingredient, that is, long memory in the aggressiveness (quantified by the relative prices) of incoming orders, which is an important stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatility synthesized from the modified MF model with the DFA scaling exponent close to 0.76, and the cubic law of returns and the diffusive behavior of prices are also produced at the same time. We also find that the long memory of order signs has no impact on the long memory property of volatility, and the memory effect of order aggressiveness has little impact on the diffusiveness of stock prices.Comment: 6 pages, 6 figures and 1 tabl