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We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical resu...
Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - dens...
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. Fo...
In this paper, we study stochastic volatility models in regimes where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the...
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail,...
We study the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models. The standard Feynman-Kac theorem cannot be directly applied ...
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is...
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatilit...
This cautious note aims to point at the potential risks for the financial system caused by various increasingly popular volatility derivatives including variance swaps on futures of equity indices. It...
In the analytical real options approach, the most important proposition that the value of the investment opportunity increases as the volatility increases has been proved by assuming the convexity of...
We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [20...
A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distrib...
We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limit...

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