5002

4706

كارشناسي ارشد

آمار رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي

1388

[شش]، 98ص: مصور، جدول، نمودار

ص. ع. به: فارسي و انگليسي

امير نادري، علي رجالي

سروش عليمرادي

13/11/88

افشين پرورده، محمد تقي جهانديده

رياضي

ID4706

به فارسي و انگليسي: قابل رويت در نسخه ديجيتال

Simulation and Inference for Stochastic Volatility Models Driven by L vy Processes e Amin Hassanzadeh amin h@math iut ac ir Oct 28 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisors Dr Amir Naderi amir@cc iut ac ir Dr Ali Rejali a rejali@cc iut ac ir2000 MSC Primary 65C20 Secondary 65C30 68U20 Key words Volatility Long memory Ornstein Uhlenbeck model Power decay model Fractional Ornstein Uhlenbeck model AbstractIn this thesis we present an expanded account of simulation and inference for stochasticvolatility models driven by L vy processes based on an article by Gander and Stephens e 2007 First we introduce stochastic volatility 2 t and long memory Ornstein Uhlenbeckmodel for volatility based on an article by Barndor Nielsen and Shephard 2001 In fact this model of 2 t should satisfy the following stochastic di erential equation d 2 t 2 t dt dZ t This model was used by Roberts et al 2004 and tted on nancial data using Bayesianmethods Later Gri n and Steel 2006 follow their works and using Markov Chain MonteCarlo for special gamma marginal law for volatility 2 t It cause to use compound Poissonprocess for subordinator Z t on above equation In 2007 Gander and Stephens follow their works in general marginal law e g generalizedinverse Gaussian GIG and tempered stable TS distributions for volatility 2 t andthen generalized Ornstein Uhlenbeck model to Wolpert and Taqqu s Telecom models 2005 such as Ornstein Uhlenbeck power decay fractional Ornstein Uhlenbeck models We study these methods and use Markov Chain Monte Carlo for these generalized models and t them using S P 500 share index data for gamma power decay and fractional Ornstein Uhlenbeck models 1

امير نادري، علي رجالي

سروش عليمرادي

افشين پرورده، محمد تقي جهانديده