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Pricing Options with Green's Functions when Volatility, Interest Rate, and Barriers Depend on Time
[journal article]
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 com... view more
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.... view less
Classification
Economic Statistics, Econometrics, Business Informatics
Basic Research, General Concepts and History of Economics
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
https://doi.org/10.1080/14697680601161480
Status
Postprint; peer reviewed
Licence
PEER Licence Agreement (applicable only to documents from PEER project)