CRIEFF Discussion Paper Number 0803
On
the qualitative effect of volatility and duration on prices of Asian options
Peter Carr (New York University), Christian-Oliver Ewald
(University of St. Andrews), Yajun Xiao (University
of Frankfurt)
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.
JEL Classifications:
G11, G31, G39, G63
Keywords:
Asian Options, Volatility, Vega, Duration, Qualitative Riskmanagement.
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