Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Option pricing with log-stable L\'{e}vy processes   We model the logarithm of the price (log-price) of a financial asset as a
random variable obtained by projecting an operator stable random vector with a
scaling index matrix $\underline{\underline{E}}$ onto a non-random vector. The
scaling index $\underline{\underline{E}}$ models prices of the individual
financial assets (stocks, mutual funds, etc.). We find the functional form of
the characteristic function of real powers of the price returns and we compute
the expectation value of these real powers and we speculate on the utility of
these results for statistical inference. Finally we consider a portfolio
composed of an asset and an option on that asset. We derive the characteristic
function of the deviation of the portfolio, \mbox{${\mathfrak D}_t^{({\mathfrak
t})}$}, defined as a temporal change of the portfolio diminished by the the
compound interest earned. We derive pseudo-differential equations for the
option as a function of the log-stock-price and time and we find exact
closed-form solutions to that equation. These results were not known before.
Finally we discuss how our solutions correspond to other approximate results
known from literature,in particular to the well known Black & Scholes equation.

14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat