Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient European and American option pricing under a jump-diffusion
  process   When the underlying asset displays oscillations, spikes or heavy-tailed
distributions, the lognormal diffusion process (for which Black and Scholes
developed their momentous option pricing formula) is inadequate: in order to
overcome these real world difficulties many models have been developed. Merton
proposed a jump-diffusion model, where the dynamics of the price of the
underlying are subject to variations due to a Brownian process and also to
possible jumps, driven by a compound Poisson process. Merton's model admits a
series solution for the European option price, and there have been a lot of
attempts to obtain a discretisation of the Merton model with tree methods in
order to price American or more complex options, e. g. Amin, the $O(n^3)$
procedure by Hilliard and Schwartz and the $O(n^{2.5})$ procedure by Dai et al.
Here, starting from the implementation of the seven-nodes procedure by Hilliard
and Schwartz, we prove theoretically that it is possible to reduce the
complexity to $O(n \ln n)$ in the European case and $O(n^2 \ln n)$ in the
American put case. These theoretical results can be obtained through suitable
truncation of the lattice structure and the proofs provide closed formulas for
the truncation limitations.

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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: math