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.
Not so Particular about Calibration: Smile Problem Resolved
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We present a novel Monte Carlo based LSV calibration algorithm that applies to all stochastic volatility models, including the non-Markovian rough volatility family. Our framework overcomes the limitations of the particle method proposed by Guyon and Henry-Labord\`ere (2012) and theoretically guarantees a variance reduction without additional computational complexity. Specifically, we obtain a closed-form and exact calibration method that allows us to remove the dependency on both the kernel function and bandwidth parameter. This makes the algorithm more robust and less prone to errors or instabilities in a production environment. We test the efficiency of our algorithm on various hybrid (rough) local stochastic volatility models.
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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.