A fast algorithm for computing integrals in function spaces: Financial applications
- 70 Downloads
The paper describes a fast and general numerical algorithm for computing path integrals in function spaces. Efficiency is ensured by use of FFT-based procedures as the primary element of the algorithm. The total number of operations required by the algorithm can be shown to be proportional to the total number of discretization nodes. A number of financial applications of the algorithm are considered, including pricing European and American style interest rate options, path dependent options, and index amortization swaps.
KeywordsInterest Rate Economic Theory Function Space Numerical Algorithm Fast Algorithm
Unable to display preview. Download preview PDF.
- 1.Chen, K.C., Karolyi, G. A., Longstaff, F.A. and Sanders, A.B., 1992, An empirical comparison of alternative models of short-term interest rates, The Journal of Finance,XLVII, No. 3, 1209–1227.Google Scholar
- 2.Dash, J., 1989, Path integrals and options, Parts I, II, Centre National de la Recherche Scientifique.Google Scholar
- 3.Kac, M., 1980, Integration in Function Spaces and Some of Its Applications, Lezioni Fermiane, Piza.Google Scholar
- 4.Hull, J. and White, A., 1992, One-factor interest rate models and the valuation of interest-rate derivative securities, University of Toronto.Google Scholar
- 5.Papuolis, A., 1977, A Signal Analysis, McGraw-Hill.Google Scholar