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- W3191010672 abstract "We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is therefore not a Markov process or semimartingale, and has quite low Holder-regularity. In practice, simulating such rough processes thus often results in high computational cost. To remedy this, we study approximations of stochastic Volterra equations using an $N$-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with superpolynomial rate in $N$. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model." @default.
- W3191010672 created "2021-08-16" @default.
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- W3191010672 date "2021-08-11" @default.
- W3191010672 modified "2023-09-27" @default.
- W3191010672 title "Makovian approximations of stochastic Volterra equations with the fractional kernel" @default.
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