Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semimartingale and continuous-time Markov chain approximation for rough
  stochastic local volatility models   Rough volatility models have recently been empirically shown to provide a
good fit to historical volatility time series and implied volatility smiles of
SPX options. They are continuous-time stochastic volatility models, whose
volatility process is driven by a fractional Brownian motion with Hurst
parameter less than half. Due to the challenge that it is neither a
semimartingale nor a Markov process, there is no unified method that not only
applies to all rough volatility models, but also is computationally efficient.
This paper proposes a semimartingale and continuous-time Markov chain (CTMC)
approximation approach for the general class of rough stochastic local
volatility (RSLV) models. In particular, we introduce the perturbed stochastic
local volatility (PSLV) model as the semimartingale approximation for the RSLV
model and establish its existence , uniqueness and Markovian representation. We
propose a fast CTMC algorithm and prove its weak convergence. Numerical
experiments demonstrate the accuracy and high efficiency of the method in
pricing European, barrier and American options. Comparing with existing
literature, a significant reduction in the CPU time to arrive at the same level
of accuracy is observed.

6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat