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

Peter Carr, Christian-Oliver Ewald and Yajun Xiao

No 803, CRIEFF Discussion Papers from Centre for Research into Industry, Enterprise, Finance and the Firm

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 Riskmanagement. (search for similar items in EconPapers)
JEL-codes: G11 G31 G39 (search for similar items in EconPapers)
Date: 2008-02
New Economics Papers: this item is included in nep-fmk, nep-rmg and nep-sea
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Citations: View citations in EconPapers (4)

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Journal Article: On the qualitative effect of volatility and duration on prices of Asian options (2008)
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