Direct computation for American put option and free boundary using finite difference method

Beom Jin Kim; Cheonghee Ahn; Hi Jun Choe

doi:10.1007/s13160-012-0094-9

Direct computation for American put option and free boundary using finite difference method

Beom Jin Kim, Cheonghee Ahn, Hi Jun Choe

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We present a direct computation scheme for pricing American put option using finite difference method (FDM) characterized by the node moving and the fixed node scale in continuation region. The work is motivated by the necessity for better understanding of the solution surface near free boundary (early exercise boundary). We exploit an intermediate function which has Lipschitz character near free boundary. The intermediate function produces a linearly converging algorithm to locate the free boundary which appears as the real root of a cubic polynomial. In conclusion, our method shows good performance in accuracy and convergence speed.

Original language	English
Pages (from-to)	21-37
Number of pages	17
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	30
Issue number	1
DOIs	https://doi.org/10.1007/s13160-012-0094-9
Publication status	Published - 2013 Feb

Bibliographical note

Funding Information:
This work was supported by BK21 project of Department of Mathematics in Yonsei University. Beom Jin Kim and H. J. Choe were supported by KRF2011-028951. C.Ahn was supported by R31-20007.

All Science Journal Classification (ASJC) codes

Engineering(all)
Applied Mathematics

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10.1007/s13160-012-0094-9

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title = "Direct computation for American put option and free boundary using finite difference method",

abstract = "We present a direct computation scheme for pricing American put option using finite difference method (FDM) characterized by the node moving and the fixed node scale in continuation region. The work is motivated by the necessity for better understanding of the solution surface near free boundary (early exercise boundary). We exploit an intermediate function which has Lipschitz character near free boundary. The intermediate function produces a linearly converging algorithm to locate the free boundary which appears as the real root of a cubic polynomial. In conclusion, our method shows good performance in accuracy and convergence speed.",

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note = "Funding Information: This work was supported by BK21 project of Department of Mathematics in Yonsei University. Beom Jin Kim and H. J. Choe were supported by KRF2011-028951. C.Ahn was supported by R31-20007.",

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N2 - We present a direct computation scheme for pricing American put option using finite difference method (FDM) characterized by the node moving and the fixed node scale in continuation region. The work is motivated by the necessity for better understanding of the solution surface near free boundary (early exercise boundary). We exploit an intermediate function which has Lipschitz character near free boundary. The intermediate function produces a linearly converging algorithm to locate the free boundary which appears as the real root of a cubic polynomial. In conclusion, our method shows good performance in accuracy and convergence speed.

AB - We present a direct computation scheme for pricing American put option using finite difference method (FDM) characterized by the node moving and the fixed node scale in continuation region. The work is motivated by the necessity for better understanding of the solution surface near free boundary (early exercise boundary). We exploit an intermediate function which has Lipschitz character near free boundary. The intermediate function produces a linearly converging algorithm to locate the free boundary which appears as the real root of a cubic polynomial. In conclusion, our method shows good performance in accuracy and convergence speed.

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Direct computation for American put option and free boundary using finite difference method

Abstract

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