### 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 |
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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