On the qualitative effect of volatility and duration on prices of Asian options
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Finance Research Letters.
Volume (Year): 5 (2008)
Issue (Month): 3 (September)
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Web page: http://www.elsevier.com/locate/frl
Asian options Volatility Vega Duration Qualitative risk-management;
Other versions of this item:
- Peter Carr & Christian-Oliver Ewald & Yajun Xiao, 2008. "On the Qualitative Effect of Volatility and Duration on Prices of Asian Options," CRIEFF Discussion Papers 0803, Centre for Research into Industry, Enterprise, Finance and the Firm.
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
- G39 - Financial Economics - - Corporate Finance and Governance - - - Other
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- Zhaojun Yang & Christian-Oliver Ewald & Olaf Menkens, 2009. "Pricing and Hedging of Asian Options: Quasi-Explicit Solutions via Malliavin Calculus," CRIEFF Discussion Papers 0910, Centre for Research into Industry, Enterprise, Finance and the Firm.
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