In this article we present new results for the pricing of arithmetic Asian options within a Black-Scholes context. To derive these results we make extensive use of the local scale invariance that exists in the theory of contingent claim pricing. This allows us to derive, in a natural way, a simple PDE for the price of arithmetic Asians options. In the case of European average strike options, a proper choice of numeraire reduces the dimension of this PDE to one, leading to a PDE similar to the one derived by Rogers and Shi. We solve this PDE, finding a Laplace-transform representation for the price of average strike options, both seasoned and unseasoned. This extends the results of Geman and Yor, who discussed the case of average price options. Next we use symmetry arguments to show that prices of average strike and average price options can be expressed in terms of each other. Finally we show, again using symmetries, that plain vanilla options on stocks paying known cash dividends are closely related to arithmetic Asians, so that all the new techniques can be directly applied to this case.
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Paper provided by EconWPA in its series Finance with number
0105002.
Length: 18 pages Date of creation: 21 May 2001 Date of revision: Handle: RePEc:wpa:wuwpfi:0105002
Note: Type of Document - Acrobat PDF; prepared on NT/LaTeX; to print on PostScript; pages: 18 ; figures: None. Contact details of provider: Web page: http://129.3.20.41
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Find related papers by JEL classification: G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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