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)

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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

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