On the qualitative effect of volatility and duration on prices of Asian options

Carr, P., Ewald, C.-O. and Xiao, Y. (2008) On the qualitative effect of volatility and duration on prices of Asian options. Finance Research Letters, 5(3), pp. 162-171. (doi: 10.1016/j.frl.2008.05.001)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ewald, Professor Christian
• Authors: Carr, P., Ewald, C.-O., and Xiao, Y.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Finance Research Letters
• ISSN: 1544-6123
• ISSN (Online): 1544-6131
• Published Online: 20 May 2008