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Two-Sided Estimates for Distribution Densities in Models with Jumps

  • Archil Gulisashvili
  • Josep Vives
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 7)

Abstract

The present paper is devoted to applications of mathematical analysis to the study of distribution densities arising in stochastic stock price models. We consider uncorrelated Stein-Stein, Heston, and Hull-White models and their perturbations by compound Poisson processes with jump amplitudes distributed according to a double exponential law. Similar perturbations of the Black-Scholes model were studied by S. Kou. For perturbed models, we obtain two-sided estimates for the stock price distribution density and compare the rate of decay of this density in the original and the perturbed model. It is shown that if the value of the parameter,characterizing the rate of decay of the right tail of the double exponential law, is small, then the stock price density in the perturbed model decays slower than the density in the original model. On the other hand, if the value of this parameter is large, then there are no significant changes in the behavior of the stock price distribution density.

Keywords

Distribution Density Stock Price Stochastic Volatility Implied Volatility Stochastic Volatility Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsOhio UniversityAthensUSA
  2. 2.Departament de Probabilitat, Lògica i EstadísticaUniversitat de BarcelonaBarcelona (Catalunya)Spain

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