On the Qualitative Effect of Volatility and Duration on Prices of Asian Options

17 Pages Posted: 24 Jan 2008

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Christian-Oliver Ewald

University of Glasgow; Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance

Yajun Xiao

University of Freiburg - Department of Economics

Date Written: January 24, 2008

Abstract

We show that under the Black Scholes assumption the price of an arithmetic average Asian call option with fixed strike increases with the level of volatility. This statement is not trivial to prove and for other models in general wrong. In fact we demonstrate that in a simple binomial model no such relationship holds. Under the Black-Scholes assumption however, we give a proof based on the maximum principle for parabolic partial differential equations. Furthermore we show that an increase in the length of duration over which the average is sampled also increases the price of an arithmetic average Asian call option, if the discounting effect is taken out. To show this, we use the result on volatility and the fact that a reparametrization in time corresponds to a change in volatility in the Black-Scholes model. Both results are extremely important for the risk management and risk assessment of portfolios that include Asian options.

Keywords: Asian options, volatility, vega, duration, qualitative risk-management

JEL Classification: C63, G11, G31, G39

Suggested Citation

Carr, Peter P. and Ewald, Christian-Oliver and Xiao, Yajun, On the Qualitative Effect of Volatility and Duration on Prices of Asian Options (January 24, 2008). Available at SSRN: https://ssrn.com/abstract=1086927 or http://dx.doi.org/10.2139/ssrn.1086927

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance ( email )

Castlecliffe
The Scores
St. Andrews, Fife KY16 9AL
United Kingdom
+44(0)1334 462435 (Phone)

HOME PAGE: http://www.maths.usyd.edu.au/u/ewald/

Yajun Xiao

University of Freiburg - Department of Economics ( email )

Freiburg, D-79085
Germany

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