Weak order one is proven for a half-step Euler discretization of local stochastic volatility dynamics, with the particle approximation error quantified in terms of step size, regularization, and number of particles.
Mimicking the marginal distributions of a semimartingale
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abstract
We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our construction applies to a large class of semimartingales, including smooth functions of a Markov process. We use this result to derive a partial integro-differential equation for the one-dimensional distributions of a semimartingale, extending the Kolmogorov forward equation to a non-Markovian setting.
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On the Weak Error for Local Stochastic Volatility Models
Weak order one is proven for a half-step Euler discretization of local stochastic volatility dynamics, with the particle approximation error quantified in terms of step size, regularization, and number of particles.