Abstract
In this paper we present an adaptive technique to solve the multi-dimensional Black–Scholes equation. The number of grid-points required for a given tolerance of the local discretization errors is reduced substantially when compared to a standard equidistant grid. Using our adaptive methods in space and time we have control of the local discretization errors and can refine the grid where needed for accuracy reasons.
Similar content being viewed by others
References
Björk T. (1998). Arbitrage Theory in Continuous Time. Oxford University Press, New York
Black F. and Scholes M. (1973). The pricing of options and corporate liabilities. J. Polit. Econ. 81: 637–659
Boyle P.P., Broadie M. and Glasserman P. (1997). Monte Carlo methods for security pricing. J. Econ. Dyn. Control 21: 1267–1321
Hairer E., Nørsett S.P. and Wanner G. (1993). Solving Ordinary Differential Equations. Springer, Berlin
Lötstedt P., Söderberg S., Ramage A. and Hemmingsson-Frändén L. (2002). Implicit solution of hyperbolic equations with space-time adaptivity. BIT 42(1): 128–153
Merton R.C. (1973). Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4: 141–183
Morton K.W. (1996). Numerical Solution of Convection-Diffusion Problems. Chapman & Hall, London
Musiela M. and Rutkowski M. (1997). Martingale Methods in Financial Modelling. Springer, Heidelberg
Saad Y. and Schultz M.H. (1986). GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. Siam J. Sci. Comp. 7: 856–869
Schwartz E.S. (1977). The valuation of warrants: implementing a new approach. J. Finan. Econ. 4: 79–93
Tavella D. and Randall C. (2000). Pricing Financial Instruments—the Finite Difference Method. Wiley, New York
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by G. Wittum.
Funded by FMB, the Graduate School in Mathematics and Computing.
An erratum to this article can be found at http://dx.doi.org/10.1007/s00791-007-0076-7
Rights and permissions
About this article
Cite this article
Persson, J., von Persson, L. Pricing European multi-asset options using a space-time adaptive FD-method. Comput. Visual Sci. 10, 173–183 (2007). https://doi.org/10.1007/s00791-007-0072-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00791-007-0072-y