Closed-form option pricing for exponential Lévy models: a residue approach

Jean-Philippe Aguilar and Justin Lars Kirkby

Quantitative Finance, 2023, vol. 23, issue 2, 251-278

Abstract: Exponential Lévy processes provide a natural and tractable generalization of the classic Black–Scholes–Merton model which account for several stylized features of financial markets, including jumps and kurtosis. In the existing literature, closed-form option pricing formulas are sparse for exponential Lévy models, outside of special cases such as Merton's jump diffusion, and complex numerical techniques are required even to price European options. To bridge the gap, this work provides a comprehensive and unified pricing framework for vanilla and exotic path independent options under the Variance Gamma (VG), Finite Moment Log Stable (FMLS), one-sided Tempered Stable (TS), and Normal Inverse Gaussian (NIG) models. We utilize the Mellin Transform and residue calculus to obtain closed-form series representations for the price of several options, including vanillas (European), digitals, power, and log options. These formulas provide nice theoretical representations, but are also efficient to evaluate in practice, as numerous numerical experiments demonstrate. The closed-form nature of these option pricing formulas makes them ideal for adoption in practical settings, as they do not require complicated pricing methods to achieve high-accuracy prices, and the resulting pricing error is reliably controllable.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/14697688.2022.2152365 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:23:y:2023:i:2:p:251-278

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697688.2022.2152365

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().