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 |
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Keywords
- Infinite variance
- Moving averages
- Nonparametric bootstrap
- Option pricing
- Point processes
- Stable laws
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
Cite this
Option pricing for infinite variance data. / Ishwaran, Hemant; Jahandideh, Mohammad T.; Zarepour, Mahmoud.
In: Statistics, Vol. 42, No. 3, 01.06.2008, p. 245-260.Research output: Contribution to journal › Article
}
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 -