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The volatility process: a study of stock market dynamics via parametric stochastic volatility models and a comparaison to the information embedded in the option price

Abstract : It is widely accepted today that an assumption of a constant standard-deviation for the stock-return is not realistic. Indeed the traditional Samuelson-Black-Scholes framework of a lognormal distribution fails to explain the existence of leptokurticity (fat tails) as well as the asymmetry (negative skew) observed in the stock-return distribution.Many different theories have been recently suggested to deal with this phenomenon, but they could all be classified under the title of Stochastic Volatility (SV). Popular SV models include GARCH, Jump-Diffusion, Heston and the Variance-Gamma models. Most of them use either Gaussian innovations with Poisson jumps or other Levy distributions such as Gamma or Ornstein-Uhlenbeck.One of the main difficulties while working with an SV model is that the actual instantaneous volatility is not observable in the market and therefore needs to be modeled as a hidden state.This means that in order to calibrate a model to the stock market, one needs to use a usually nonlinear and/ or non-Gaussian Filter. An alternative would be to use a Bayesian Markov-Chain Monte-Carlo approach. This calibration will then provide us with an estimation of the statistical (or real-world) distribution of the stock-return.This thesis focuses on Nonlinear and Non-Gaussian Filtering as well as the comparison between the Statistical and Risk-Neutral distributions.
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Submitted on : Wednesday, May 14, 2008 - 8:00:00 AM
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Alireza Javaheri. The volatility process: a study of stock market dynamics via parametric stochastic volatility models and a comparaison to the information embedded in the option price. Humanities and Social Sciences. École Nationale Supérieure des Mines de Paris, 2004. English. ⟨NNT : 2004ENMP1250⟩. ⟨pastel-00003319⟩

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