Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetries in jump-diffusion models with applications in option pricing
  and credit risk   It is a well known fact that local scale invariance plays a fundamental role
in the theory of derivative pricing. Specific applications of this principle
have been used quite often under the name of `change of numeraire', but in
recent work it was shown that when invoked as a fundamental first principle, it
provides a powerful alternative method for the derivation of prices and hedges
of derivative securities, when prices of the underlying tradables are driven by
Wiener processes. In this article we extend this work to the pricing problem in
markets driven not only by Wiener processes but also by Poisson processes, i.e.
jump-diffusion models. It is shown that in this case too, the focus on symmetry
aspects of the problem leads to important simplifications of, and a deeper
insight into the problem. Among the applications of the theory we consider the
pricing of stock options in the presence of jumps, and Levy-processes. Next we
show how the same theory, by restricting the number of jumps, can be used to
model credit risk, leading to a `market model' of credit risk. Both the
traditional Duffie-Singleton and Jarrow-Turnbull models can be described within
this framework, but also more general models, which incorporate default
correlation in a consistent way. As an application of this theory we look at
the pricing of a credit default swap (CDS) and a first-to-default basket
option.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn