The Finite Moment Log Stable Process and Option Pricing

Peter Carr, Liuren Wu

Research output: Contribution to journalArticle

Abstract

We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.

Original languageEnglish (US)
Pages (from-to)753-777
Number of pages25
JournalJournal of Finance
Volume58
Issue number2
DOIs
StatePublished - Apr 2003

Fingerprint

Implied volatility
Maturity
Central limit theorem
Option pricing
Calibration
Option prices
Asymptotic behavior
Exercise

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Economics and Econometrics

Cite this

The Finite Moment Log Stable Process and Option Pricing. / Carr, Peter; Wu, Liuren.

In: Journal of Finance, Vol. 58, No. 2, 04.2003, p. 753-777.

Research output: Contribution to journalArticle

Carr, Peter ; Wu, Liuren. / The Finite Moment Log Stable Process and Option Pricing. In: Journal of Finance. 2003 ; Vol. 58, No. 2. pp. 753-777.
@article{a59e2dabd3b64b509d90c11215534c23,
title = "The Finite Moment Log Stable Process and Option Pricing",
abstract = "We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.",
author = "Peter Carr and Liuren Wu",
year = "2003",
month = "4",
doi = "10.1111/1540-6261.00544",
language = "English (US)",
volume = "58",
pages = "753--777",
journal = "Journal of Finance",
issn = "0022-1082",
publisher = "Wiley-Blackwell",
number = "2",

}

TY - JOUR

T1 - The Finite Moment Log Stable Process and Option Pricing

AU - Carr, Peter

AU - Wu, Liuren

PY - 2003/4

Y1 - 2003/4

N2 - We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.

AB - We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.

UR - http://www.scopus.com/inward/record.url?scp=0142219274&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142219274&partnerID=8YFLogxK

U2 - 10.1111/1540-6261.00544

DO - 10.1111/1540-6261.00544

M3 - Article

VL - 58

SP - 753

EP - 777

JO - Journal of Finance

JF - Journal of Finance

SN - 0022-1082

IS - 2

ER -