An Analysis of Path-Dependent Options

Frank Wusterhausen ()
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Frank Wusterhausen: Martin Luther University Halle-Wittenberg

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 3, No 7, 874-887

Abstract: Abstract The objective of this paper is to provide an analytic theory for pricing path-dependent options of European type. General conditions for the path-dependencies are introduced, which allow a wide range of application. We present a partial differential equation describing the fair price process of a path-dependent option in a Black–Scholes world, where the classical Black–Scholes equation involves additional terms caused by the path-dependency of the option. The main result is that the problem is well posed in appropriate function spaces.

Keywords: Path-dependent options; Black–Scholes; Elliptic–hyperbolic partial differential equation; Noncommuting sums of operators; Semigroup methods (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-013-0405-6

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