New Unified Computational Algorithm in a High-Order Asymptotic Expansion Scheme ( Forthcoming in "The Proceedings of KIER-TMU International Workshop on Financial Engineering 2009".)
AbstractAn asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi  and Yoshida  is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. Mathematically, this methodology is justified by Watanabe theory () in Malliavin calculus. In practical applications, it is desirable to investigate the accuracy and stability of the method especially with expansion up to high orders in situations where the underlying processes are highly volatile as seen in the recent financial markets. Although Takahashi ,  and Takahashi and Takehara  provided explicit formulas for the expansion up to the third order, to our best knowledge a general computation scheme for an arbitraryorder expansion has not been given yet. This paper proposes two general methods for computing the conditional expectations that are powerful especially for high order expansions: The first one, as an extension of the method introduced by the preceding papers, presents a unified scheme for computation of the conditional expectations. The second one develops a new calculation algorithm for computing the coefficients of the expansion through solving a system of ordinary differential equations that is equivalent to computing the conditional expectations. To demonstrate their effectiveness, the paper gives numerical examples of the approximation for Lambda-SABR model up to the fifth order and a cross-currency Libor market model with a general stochastic volatility model of the spot foreign exchange rate up to the fourth order.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-212.
Length: 18 pages
Date of creation: Mar 2010
Date of revision:
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Masaaki Fujii & Akihiko Takahashi, 2011. "Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA," CARF F-Series CARF-F-265, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.