Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility
Masaaki Fujii and
Additional contact information
Masaaki Fujii: Faculty of Economics, The University of Tokyo
Akihiko Takahashi: Faculty of Economics, The University of Tokyo
No CARF-F-270, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo
In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we derive explicit expression for the solution of the FBSDE up to the third order of volatility-of-volatility, which can be directly translated into the optimal investment strategy. We compare our approximation with the exact solution, which is known to be derived by the Cole-Hopf transformation in this popular setup. The result is very encouraging and shows good accuracy of the approximation up to quite long maturities. Since our new methodology can be extended straightforwardly to multi-dimensional setups, we expect it will open real possibilities to obtain explicit optimal portfolios or hedging strategies under realistic assumptions.
Date: 2012-02, Revised 2012-06
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (12) Track citations by RSS feed
Downloads: (external link)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf270
Access Statistics for this paper
More papers in CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by ().