## A critical analysis of risk and volatility modeling in the financial markets

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2011-12-20##### Author

Moloney, Catherine (Kitty)

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##### Abstract

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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