Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Closed-Form Approximation of Likelihood Functions for Discretely
  Sampled Diffusions: the Exponent Expansion   In this paper we discuss a closed-form approximation of the likelihood
functions of an arbitrary diffusion process. The approximation is based on an
exponential ansatz of the transition probability for a finite time step $\Delta
t$, and a series expansion of the deviation of its logarithm from that of a
Gaussian distribution. Through this procedure, dubbed {\em exponent expansion},
the transition probability is obtained as a power series in $\Delta t$. This
becomes asymptotically exact if an increasing number of terms is included, and
provides remarkably accurate results even when truncated to the first few (say
3) terms. The coefficients of such expansion can be determined
straightforwardly through a recursion, and involve simple one-dimensional
integrals.
  We present several examples of financial interest, and we compare our results
with the state-of-the-art approximation of discretely sampled diffusions
[A\"it-Sahalia, {\it Journal of Finance} {\bf 54}, 1361 (1999)]. We find that
the exponent expansion provides a similar accuracy in most of the cases, but a
better behavior in the low-volatility regime. Furthermore the implementation of
the present approach turns out to be simpler.
  Within the functional integration framework the exponent expansion allows one
to obtain remarkably good approximations of the pricing kernels of financial
derivatives. This is illustrated with the application to simple path-dependent
interest rate derivatives. Finally we discuss how these results can also be
used to increase the efficiency of numerical (both deterministic and
stochastic) approaches to derivative pricing.

1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th