Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Binomial Tree Method and Explicit Difference Schemes for American
  Options with Time Dependent Coefficients   Binomial tree methods (BTM) and explicit difference schemes (EDS) for the
variational inequality model of American options with time dependent
coefficients are studied. When volatility is time dependent, it is not
reasonable to assume that the dynamics of the underlying asset's price forms a
binomial tree if a partition of time interval with equal parts is used. A time
interval partition method that allows binomial tree dynamics of the underlying
asset's price is provided. Conditions under which the prices of American option
by BTM and EDS have the monotonic property on time variable are found. Using
convergence of EDS for variational inequality model of American options to
viscosity solution the decreasing property of the price of American put options
and increasing property of the optimal exercise boundary on time variable are
proved. First, put options are considered. Then the linear homogeneity and
call-put symmetry of the price functions in the BTM and the EDS for the
variational inequality model of American options with time dependent
coefficients are studied and using them call options are studied.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph