FVA and CVA under margining
Abstract
Purpose
The purpose of this paper is to provide a framework of replication pricing of derivatives and identify funding valuation adjustment (FVA) and credit valuation adjustments (CVA) as price components.
Design/methodology/approach
The authors propose the notion of bilateral replication pricing. In the absence of funding cost, it reduces to unilateral replication pricing. The absence of funding costs, it introduces bid–ask spreads.
Findings
The valuation of CVA can be separated from that of FVA, so-called split up. There may be interdependence between FVA and the derivatives value, which then requires a recursive procedure for their numerical solution.
Research limitations/implications
The authors have assume deterministic interest rates, constant CDS rates and loss rates for the CDS. The authors have also not dealt with re-hypothecation risks.
Practical implications
The results of this paper allow user to identify CVA and FVA, and mark to market their derivatives trades according to the recent market standards.
Originality/value
For the first time, a line between the risk-neutral pricing measure and the funding risk premiums is drawn. Also, the notion of bilateral replication pricing extends the unilateral replication pricing.
Keywords
Acknowledgements
This research has been funded by RGC/UGC grant FSGRF13SC19. Parts of this paper have been presented in The World Congress of Bachelier Finance Society, June 2012, Sydney; Mathematical Finance Seminar in Imperial College, October 2012, London; Workshop on Stochastic Control and Financial Applications by AMSS-PolyU Joint Research Institute, December 2012, Hong Kong; The First Asian Quantitative Finance Conference, January 2013, Singapore; International Workshop on Finance Engineering, Meiji University, March 2013, Tokyo; International Conference on Financial Engineering and Innovation, March 2014, Shanghai; and International Symposium on Partial Differential Equations and Stochastic Analysis in Mathematical Finance, July 2014, Sanya, China. The authors would like to thank Damiano Brigo, John Hull, Fabio Mercurio, Eckhard Platen and Ken Yan for their helpful comments. All remaining errors are that of the authors.
Citation
Wu, L. and Li, C. (2015), "FVA and CVA under margining", Studies in Economics and Finance, Vol. 32 No. 3, pp. 298-321. https://doi.org/10.1108/SEF-08-2014-0162
Publisher
:Emerald Group Publishing Limited
Copyright © 2015, Emerald Group Publishing Limited