Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multilevel Monte Carlo simulation for VIX options in the rough Bergomi
  model   We consider the pricing of VIX options in the rough Bergomi model [Bayer,
Friz, and Gatheral, Pricing under rough volatility, Quantitative Finance 16(6),
887-904, 2016]. In this setting, the VIX random variable is defined by the
one-dimensional integral of the exponential of a Gaussian process with
correlated increments, hence approximate samples of the VIX can be constructed
via discretization of the integral and simulation of a correlated Gaussian
vector. A Monte-Carlo estimator of VIX options based on a rectangle
discretization scheme and exact Gaussian sampling via the Cholesky method has a
computational complexity of order $\mathcal O(\varepsilon^{-4})$ when the
mean-squared error is set to $\varepsilon^2$. We demonstrate that this cost can
be reduced to $\mathcal O(\varepsilon^{-2} \log^2(\varepsilon))$ combining the
scheme above with the multilevel method [Giles, Multilevel Monte Carlo path
simulation, Oper. Res. 56(3), 607-617, 2008], and further reduced to the
asymptotically optimal cost $\mathcal O(\varepsilon^{-2})$ when using a
trapezoidal discretization. We provide numerical experiments highlighting the
efficiency of the multilevel approach in the pricing of VIX options in such a
rough forward variance setting.

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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn