Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Efficiency of 5(4) RK-Embedded Pairs with High Order Compact
  Scheme and Robin Boundary Condition for Options Valuation   When solving the American options with or without dividends, numerical
methods often obtain lower convergence rates if further treatment is not
implemented even using high-order schemes. In this article, we present a fast
and explicit fourth-order compact scheme for solving the free boundary options.
In particular, the early exercise features with the asset option and option
sensitivity are computed based on a coupled of nonlinear PDEs with fixed
boundaries for which a high order analytical approximation is obtained.
Furthermore, we implement a new treatment at the left boundary by introducing a
third-order Robin boundary condition. Rather than computing the optimal
exercise boundary from the analytical approximation, we simply obtain it from
the asset option based on the linear relationship at the left boundary. As
such, a high order convergence rate can be achieved. We validate by examples
that the improvement at the left boundary yields a fourth-order convergence
rate without further implementation of mesh refinement, Rannacher
time-stepping, and/or smoothing of the initial condition. Furthermore, we
extensively compare, the performance of our present method with several 5(4)
Runge-Kutta pairs and observe that Dormand and Prince and Bogacki and Shampine
5(4) pairs are faster and provide more accurate numerical solutions. Based on
numerical results and comparison with other existing methods, we can validate
that the present method is very fast and provides more accurate solutions with
very coarse grids.

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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph