### Abstract

Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a θ-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary, and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.

Original language | English |
---|---|

Pages (from-to) | 413-426 |

Number of pages | 14 |

Journal | Bulletin of the Korean Mathematical Society |

Volume | 48 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 Apr 29 |

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### Keywords

- American options
- Binary options
- Hybrid finite difference method
- Option pricing
- Variable time steps

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the Korean Mathematical Society*,

*48*(2), 413-426. https://doi.org/10.4134/BKMS.2011.48.2.413

**Variable time-stepping hybrid finite difference methods for pricing binary options.** / Kim, Hongjoong; Moon, Kyoung Sook.

Research output: Contribution to journal › Article

*Bulletin of the Korean Mathematical Society*, vol. 48, no. 2, pp. 413-426. https://doi.org/10.4134/BKMS.2011.48.2.413

}

TY - JOUR

T1 - Variable time-stepping hybrid finite difference methods for pricing binary options

AU - Kim, Hongjoong

AU - Moon, Kyoung Sook

PY - 2011/4/29

Y1 - 2011/4/29

N2 - Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a θ-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary, and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.

AB - Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a θ-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary, and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.

KW - American options

KW - Binary options

KW - Hybrid finite difference method

KW - Option pricing

KW - Variable time steps

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UR - http://www.scopus.com/inward/citedby.url?scp=79955138008&partnerID=8YFLogxK

U2 - 10.4134/BKMS.2011.48.2.413

DO - 10.4134/BKMS.2011.48.2.413

M3 - Article

AN - SCOPUS:79955138008

VL - 48

SP - 413

EP - 426

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

SN - 1015-8634

IS - 2

ER -