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چكيده انگليسي :

Computing Value at Risk using the Dirichlet Process Neda Esmaeeli n esmaeeli@math iut ac ir Janury 20 2010 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisors Dr Mohamad Taghi Jahandideh jahandid@cc iut ac ir 2000 MSC 62P05 Key words Value at Risk Return Quantile Dirichlet process Bayes estimate Abstract Rapid globalization innovation in the design of derivative securities and examples of spectacular losses associated with derivatives over the past decade have made rms recognize the growing importance of risk management This increased focus on risk management has led to the development of various methods and tools to measure the risks rms face One popular risk measurement tool is Value at Risk VaR which is de ned as the maximal amount that may be lost in a portfolio over a given period of time at a certain con dence level In this thesis we compute VaR using the Dirichlet process based on the article by Mahmoud Zarepour Thierry Bedard Andre R Dabrowski june 2008 Statistically speaking the VaR of a portfolio is the quantile of the distribution of returns Return is de ned as the logarithm of ratio of the asset prices The fact that returns need not follow the distribution speci ed in any speci c model is a signi cant limitation The goal of this thesis is to develop an adaptive method of estimating VaR in nancial markets for a random walk setting i i d returns but where we avoid specifying the distribution the returns We introduce an alternative methodology to simulate these returns by using a Montecarlo simulation of the Dirichlet process and estimate the quantile of these simulated returns This is a Bayesian approach that uses the past data directly in the simulation of asset price evolution and thereby avoids choosing a particular model for the asset price The analyst s experience enters into the method through a prior guess for the distribution of Y and the degree of con dence he has in the prior distribution As with all Bayesian procedures past data is used to update the prior distribution The posterior distribution is then used to simulate future market behavior and perhaps to produce a credible con dence interval for VaR We then estimate VaR produced by this method particularly for cases where tails of the distribution for returns are assumed to be heavy for example stable Finally we establish that the produced estimation is a consistent estimator of VaR The simulation study given here will show that the Dirichlet process methodology is a exible alternative to model based methods that loses little for large historical data sets and perhaps is better on short period horizons Just as with other machine learning algorithms this Bayesian procedure adapts to the information provided by the data and so can correct for the analysts poor initial guess as to the form of the distribution of innovations The model is constructed in a Bayesian framework using properties initially described by Ferguson 1973 The method is relatively automatic and similar to machine learning tools 1

اسماعيلي، ندا

محاسبه ارزش در معرض خطر با استفاده ار فرآيند دريكله

بازدهي سرمايه , چندك , برآورد بيز