SUBLEADING CORRECTION TO THE ASIAN OPTIONS VOLATILITY IN THE BLACK–SCHOLES MODEL

Dan Pirjol ()
Additional contact information
Dan Pirjol: School of Business, Stevens Institute of Technology, Hoboken, NJ 07030, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 02n03, 1-19

Abstract: The short maturity limit T → 0 for the implied volatility of an Asian option in the Black–Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note, we derive the subleading O(T) correction to this implied volatility, using an asymptotic expansion for the Hartman–Watson distribution. The result is used to compute subleading corrections to Asian options prices in a small maturity expansion, sharpening the leading order result obtained using large deviations theory. We demonstrate good numerical agreement with precise benchmarks for Asian options pricing in the Black–Scholes model.

Keywords: Asymptotic expansions; Asian options; time integral of the geometric Brownian motion (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S021902492350005X
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:wsi:ijtafx:v:26:y:2023:i:02n03:n:s021902492350005x

Ordering information: This journal article can be ordered from

DOI: 10.1142/S021902492350005X

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().