### 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

**Option pricing for infinite variance data.** / Ishwaran, Hemant; Jahandideh, Mohammad T.; Zarepour, Mahmoud.

Research output: Contribution to journal › Article

*Statistics*, vol. 42, no. 3, pp. 245-260. https://doi.org/10.1080/02331880701830748

}

TY - JOUR

T1 - Option pricing for infinite variance data

AU - Ishwaran, Hemant

AU - Jahandideh, Mohammad T.

AU - Zarepour, Mahmoud

PY - 2008/6/1

Y1 - 2008/6/1

N2 - 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.

AB - 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.

KW - Infinite variance

KW - Moving averages

KW - Nonparametric bootstrap

KW - Option pricing

KW - Point processes

KW - Stable laws

UR - http://www.scopus.com/inward/record.url?scp=45749135462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45749135462&partnerID=8YFLogxK

U2 - 10.1080/02331880701830748

DO - 10.1080/02331880701830748

M3 - Article

AN - SCOPUS:45749135462

VL - 42

SP - 245

EP - 260

JO - Statistics

JF - Statistics

SN - 0233-1888

IS - 3

ER -