Abstract
The objective of this paper is to provide an analytic theory for pricing of Asian options of European type. We present a partial differential equation describing the fair price process of an Asian option. This appears as
and the associated payoff function as the end value. Here the operator A is the d-dimensional Black-Scholes operator, and B = x·∇ y represents the path dependence in terms of the price averaging in Asian options. The main result will be to prove, that a solution of this partial differential equation exists, is unique, and depends continuously on the data in appropriate function spaces, i.e., that the problem is well posed. On our way we are going to employ semigroup methods, in particular the Lumer-Phillips theorem.
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References
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Dedicated to the memory of Günter Lumer
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Prüss, J., Sperlich, S., Wilke, M. (2007). An Analysis of Asian options. In: Amann, H., Arendt, W., Hieber, M., Neubrander, F.M., Nicaise, S., von Below, J. (eds) Functional Analysis and Evolution Equations. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7794-6_33
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DOI: https://doi.org/10.1007/978-3-7643-7794-6_33
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7793-9
Online ISBN: 978-3-7643-7794-6
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