Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Option pricing with fractional stochastic volatility and discontinuous
  payoff function of polynomial growth   We consider the pricing problem related to payoffs that can have
discontinuities of polynomial growth. The asset price dynamic is modeled within
the Black and Scholes framework characterized by a stochastic volatility term
driven by a fractional Ornstein-Uhlenbeck process. In order to solve the
aforementioned problem, we consider three approaches. The first one consists in
a suitable transformation of the initial value of the asset price, in order to
eliminate possible discontinuities. Then we discretize both the Wiener process
and the fractional Brownian motion and estimate the rate of convergence of the
related discretized price to its real value, the latter one being impossible to
be evaluated analytically. The second approach consists in considering the
conditional expectation with respect to the entire trajectory of the fractional
Brownian motion (fBm). Then we derive a closed formula which involves only
integral functional depending on the fBm trajectory, to evaluate the price;
finally we discretize the fBm and estimate the rate of convergence of the
associated numerical scheme to the option price. In both cases the rate of
convergence is the same and equals $n^{-rH}$, where $n$ is a number of the
points of discretization, $H$ is the Hurst index of fBm, and $r$ is the
H\"{o}lder exponent of volatility function. The third method consists in
calculating the density of the integral functional depending on the trajectory
of the fBm via Malliavin calculus also providing the option price in terms of
the associated probability density.

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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph