Modelling Extreme Financial Risks With Stochastic Volatility

Since the Sub-Mortgage Crisis of 2008,people have realized that there was severe underestimation on the possibility of extreme financial risks and their potential damages.More concern has been raised because risk managers usually lack effective tools to deal with this kind of risks,which lead to huge losses almost inevitably.Total Risk Management Theory suggests that extreme financial risks should be included to the whole management process and be dealt with.Since then,extreme financial risks have become one of the hottest topics in risk management.Risk quantification is the core and the first step of the whole process in risk management.According to the scope of the influence,the extreme risks in financial markets can be quantified on two levels.On a single market level:taking a stock market for example,the prices of stocks rise or fall outside a pre-defined area can be recognized as an extreme risk event,usually we estimated the losses and use it to measure the risk.So the higher the losses are,the bigger the risk is.For two markets or more,instead of calculating estimated losses,people are more concerned with the possibility of causing a risk contagion.Here we use tail dependence to describe the possibility of having risk contagion.The higher the tail dependence is,the bigger the possibility for a risk contaminate.In this dissertation,we develop several risk measuring models on the two risk levels.For a single market situation,we construct our model by following the routine,using the time series of stock index prices to fit its tail distribution and calculate its risk measurement.During this process,the following steps are needed,first of all,we adopt a stochastic volatility model to estimate the volatility,then we use Extreme Value Theory to describe the tail distribution,finally we choose a proper risk measurement method to calculate the risk.We make several improvements according to the process,including:(1)we construct a SV-POT-TDRM extreme risk model using TDRM methods instead of VaR to calculate the risk.Since VaR only considers the quantile point of the tail distribution which tends to underestimate the tail risk,here we construct a SV-POT-TDRM model by introducing tail distortion risk measurement from actuarial studies,combining with stochastic volatility model and extreme value theory.The main feature of this new model is it can estimate the tail risk more adequately,and it can also reflect market participants' different risk preferences by changing distortion functions or the parameters of the functions.Which means when people's risk aversion increases with the level of the losses,the risk measurement also increases accordingly.(2)We construct a MSSV-POT-TDRM extreme risk model to reflect the regime-switching characteristics of the volatility and calculate risk measurement.The parameters of a volatility model often show structural changes during different market conditions which implies using one set of parameters may not be appropriate.Basic SV model can't reflect this characteristic and shows "quasi-consistent" phenomenon.In order to fix this,we introduce a Markov process to the parameters of SV model.Combining POT and TDRM methods,we construct a MSSV-POT-TDRM model and use it to calculate the tail risk?(3)In order to predict the short-term extreme risk,we extract shape parameter of the tail distribution from daily trading data of put options,and examine its prediction power as an indicator.Under the risk-neutral measurement,using extreme value theory,we can extract tail shape parameter from out-of-the-value put option data traded in daily market and adopt a single-variable logistic model to examine its prediction power over short-term extreme risk.The practical studies find that as an indicator,the shape parameter shows good prediction power in three short-term windows which is better than the other three indicators also extracted from option data(including implied volatility,implied skewness and implied kurtosis).A Multivariable Logistic Model is adopted to examine the prediction power of 4 indicators together as dependent variables.The results show that the explaining power of the model has been improved dramatically which implies each indicator may contain different information.For the multi-markets situation,we study the tail dependence among several markets by separating it into two parts:tail distribution of each market and their dependence structure.First of all,a SV-POT model is implemented to fit each tail distribution.Then a multivariate conditional tail dependence model is constructed to describe their dependence structure.It is worth noticing that the tail dependence is calculated as a probability to examine how the rest markets behavior when one of the markets suffers a crisis.The rest markets may suffer crisis or remain normal.Comparing to other methods that only use joint distributions such as Copula methods,the model implemented here use more information.Our models can be used in several cases,from an investor's point of view,these models can help them know more about the risks of their assets;from a regulator's point of view,these models can be used to monitor the systemic risk in terms of risk management tools.