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We introduce a class of local stochastic volatility models.Within our framework, we obtain an expression for both (i) the price of any European option and (ii) the induced implied volatility smile. To...
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pri...
Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter $\gamma$ takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the...
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method...
Considering a production economy with an arbitrary von-Neumann Morgenstern utility, this paper derives a general equilibrium relationship between the market prices of risks and market risk aversion un...
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...
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise t...
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model.To be more specific, we consider the conditional expectation of vari...
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 ...
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...
We show that in a large class of stochastic volatility models with additional skew-functions (local-stochastic volatility models) the tails of the cumulative distribution of the log-returns behave as...
We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still ...
The stochastic exponential Zt = exp{Mt M0 − (1/2)hM,Mit} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the ...

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