### Abstract

Adaptive lattice methods are developed to compute the price of multivariate contingent claims. A simple coordinate representation is used to extend one dimensional lattice methods to multivariate asset models. Two algorithms are proposed, one performing several levels of refinement for a time interval [T - Δ t, T] and the other performing one level of refinement for λ % of a given time domain [0, T], where T is the time to maturity, Δ t is the time step size and λ > 0 is a constant. Numerical experiments are carried out for the European and American barrier-type options with one, two, or three underlying assets. In our numerical experiments, both adaptive algorithms improve efficiency over lattice methods with a uniform time step for the same level of accuracy.

Original language | English |
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Pages (from-to) | 352-366 |

Number of pages | 15 |

Journal | Computers and Mathematics with Applications |

Volume | 56 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Jul 1 |

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### Keywords

- Adaptive mesh refinement
- Lattice method
- Multi-asset option pricing

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

*Computers and Mathematics with Applications*,

*56*(2), 352-366. https://doi.org/10.1016/j.camwa.2007.12.008