A critical analysis of risk and volatility modeling in the financial markets
Moloney, Catherine (Kitty)
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In light of the recent financial crisis, the limitations of current risk estimation techniques have become apparent. The purpose of this thesis is to see if nonlinear tools and techniques can facilitate our understanding of the financial markets, particularly during times of heightened turbulence. This is done by comparing econometric and nonlinear tools to analyse a number of asset classes, including equities, bonds and credit default swaps during periods of heightened turbulence. We analyse indices as well as individual corporate and sovereign securities. The methodology is to compare the linear stochastic framework (in particular the linear Gaussian framework) to the nonlinear time series framework. In essence the focus of the thesis is on the treatment of irregularity by these two very different frameworks. The linear stochastic framework treats irregularity as exogenous from the linear system, and expresses it in terms of probability distribution functions. The nonlinear time series framework allows the irregularity to be part of the system i.e. endogenous. The thesis is divided into five chapters, an introduction and conclusion chapter, and three chapters which represent three papers. The abstracts of the three papers i.e. chapters 2, 3 and, 4 are presented here. The objective of chapter two is to test for nonlinear dependence in the GARCH residuals of a number of asset classes using nonlinear dynamic tools. The equity and bond market samples appear to be independent once GARCH has been applied but evidence of nonlinear dependence in the CDS GARCH residuals is found. The sensitivity of this result is analysed by changing the specifications of the GARCH model and the robustness of the result is verified by applying additional tests of nonlinearity; that is delay plots and the correlation dimension test. Evidence of nonlinear dependence in the GARCH residuals of CDS contracts has implications for the accurate modeling of the marginal distribution of the CDS market, for pricing of CDS contracts, for estimating risk neutral default probabilities in the bond market as well as for bond market hedging strategies. Chapter 3 considers the arbitrage-free parity theory. This theory states that there will be equivalence between credit default swap (CDS) spreads and bond market spreads in equilibrium. In this chapter, we test this theory using linear and nonlinear tools. Linear stochastic modeling is reviewed, particularly the assumptions of a Gaussian distribution and of iid and stationary residuals. By applying the nonlinear dynamic tools of Cross Recurrence Plots and Cross Recurrence Plot measures, evidence of dynamically varying convergence and statistically consistent synchronization across the markets is illustrated. There is evidence that the arbitrage-free parity is conditional and equivalence is non-mean reverting. In particular there is evidence of a rising trend in equivalence in the Greek sovereign market prior to the bailout of May 2010. This trend indicates increased arbitrage activity at this time. Applying a nonlinear analysis of the markets significantly increases our understanding of the dynamically varying relationship between these two assets classes. This result has implications for supervision of arbitrage activity and for financial market policy making. In chapter four, application of the nonlinear dynamical tool, recurrence quantification analysis (RQA) presents some evidence of periodic to chaotic transitions and bifurcation points at localized peaks of the Dow Jones Industrial Index. There is also evidence of a collapse in all the RQA measures just as the market transitions from bull to bear market. This suggests that the market becomes completely unpredictable at this time. We suggest the market is intermittently or piecewise deterministic and that the unpredictable regime allows the market dynamics to break from the past. The noisy trader theory is suggested as the economic explanation for this unpredictability. We develop a principal component series and name it the random market indicator (RMI). We suggest that this series indicates when the market is transitioning into and out of a nonstationary random regime. During this time, quantitative risk estimation techniques, such as value at risk models will produce misleading results.
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