### Abstract

We consider the asymptotic option pricing formula under an infinite variance paradigm using a randomized version of the Cox-Ross-Rubinstein binomial option pricing approach. We discuss practical difficulties in applying the asymptotic formula and suggest a non-parametric bootstrap as an estimation technique. Using point process theory, the asymptotic consistency of the bootstrap approach is established under a resampling scheme of m=o(n). We briefly discuss extensions to correlated data and show the option pricing formula may no longer be valid in such settings. Finally, we consider a finite variance setting involving innovations from a variance gamma process. We derive the asymptotic option pricing formula and show that the non-parametric bootstrap is consistent.

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

Pages (from-to) | 245-260 |

Number of pages | 16 |

Journal | Statistics |

Volume | 42 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

- Infinite variance
- Moving averages
- Nonparametric bootstrap
- Option pricing
- Point processes
- Stable laws

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Statistics*,

*42*(3), 245-260. https://doi.org/10.1080/02331880701830748