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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...
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...
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 ...
Probabilistic representations of the density function of the asset price and of vanilla options in linear stochastic volatility models
In usual stochastic volatility models, the process driving the volatility of the asset price evolves accord-ing to an autonomous one-dimensional stochastic differential equation. We assume that the co...

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