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Pricing Options with Green's Functions when Volatility, Interest Rate, and Barriers Depend on Time

[journal article]

Dorfleitner, Gregor; Schneider, Paul; Hawlitschek, Kurt; Buch, Arne

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Please use the following Persistent Identifier (PID) to cite this document:http://nbn-resolving.de/urn:nbn:de:0168-ssoar-220985

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Abstract We derive the Green's function for the Black/Scholes partial differential equation with time-varying coefficients and time-dependent boundary conditions. We provide a thorough discussion of its implementation within a pricing algorithm that also accommodates American style options. Greeks can be computed as derivatives of the Green's function. Generic handling of arbitrary time-dependent boundary conditions suggests our approach to be used with the pricing of (American) barrier options, although options without barriers can be priced equally well. Numerical results indicate that knowledge of the structure of the Green's function together with the well developed tools of numerical integration make our approach fast and numerically stable.
Classification Basic Research, General Concepts and History of Economics; Economic Statistics, Econometrics, Business Informatics
Method theory application
Free Keywords Green's function; Time-dependent coefficients; Numerical methods; Option pricing; (Double) barrier options; American options
Document language English
Publication Year 2008
Page/Pages p. 119-133
Journal Quantitative Finance, 8 (2008) 2
DOI http://dx.doi.org/10.1080/14697680601161480
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)