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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...
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...
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 ...
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 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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