What is the volatility of an Asian option?

Risk, May 2021 Issue, 74-79

16 Pages Posted: 8 Jul 2021 Last revised: 21 Jul 2021

See all articles by Dan Pirjol

Dan Pirjol

Stevens Institute of Technology

Lingjiong Zhu

Florida State University

Date Written: June 29, 2021

Abstract

We propose a simple approximation for pricing Asian options on an underlying asset with an implied volatility smile by substituting an appropriately adjusted volatility into a Black-Scholes pricer which takes a constant volatility. For Asian options with strikes close to the at-the-money point, the adjustment is independent of the shape of the volatility smile at leading order in an expansion in log-strike, which makes it robust against calibration errors. The smile adjusted valuation becomes exact for Asian options with continuous time averaging in the short maturity limit in the local volatility model.

Keywords: Asian options, implied volatility, approximation, short maturity

JEL Classification: G13

Suggested Citation

Pirjol, Dan and Zhu, Lingjiong, What is the volatility of an Asian option? (June 29, 2021). Risk, May 2021 Issue, 74-79, Available at SSRN: https://ssrn.com/abstract=3875929 or http://dx.doi.org/10.2139/ssrn.3875929

Dan Pirjol (Contact Author)

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Lingjiong Zhu

Florida State University ( email )

Tallahasse, FL 32306
United States

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