Imperial College London

ProfessorDamianoBrigo

Faculty of Natural SciencesDepartment of Mathematics

Chair in Mathematical Finance
 
 
 
//

Contact

 

damiano.brigo

 
 
//

Location

 

805Weeks BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Brigo:2019:10.1016/j.ejor.2018.10.046,
author = {Brigo, D and Francischello, M and Pallavicini, A},
doi = {10.1016/j.ejor.2018.10.046},
journal = {European Journal of Operational Research},
pages = {788--805},
title = {Nonlinear valuation under credit, funding, and margins: existence, uniqueness, invariance, and disentanglement},
url = {http://dx.doi.org/10.1016/j.ejor.2018.10.046},
volume = {274},
year = {2019}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - Since the 2008 global financial crisis, the banking industry has been using valuation adjustments to account for default risk and funding costs. These adjustments are computed separately and added together by practitioners as if the valuation equations were linear. This assumption is too strong and does not allow to model market features such as different borrowing and lending rates and replacement default closeout. Hence we argue that the full valuation equations are nonlinear, and this paper is devoted to studying the nonlinear valuation equations introduced in Pallavicini et al (2011).We illustrate all the cash flows exchanged by the parties involved in a derivative contract, in presence of default risk, collateralisation with re-hypothecation and funding costs. Then we show how to obtain semi-linear PDEs or Forward Backward Stochastic Differential Equations (FBSDEs) from present-valuing said cash flows in an arbitrage-free setup, and we study the well-posedness of these PDEs and FBSDEs in a viscosity and classical sense.Moreover, from a financial perspective, we discuss cases where classical valuation adjustments (XVA) can be disentangled. We show how funding costs are offset by treasury valuation adjustments when one takes a whole-bank perspective in the valuation, while the same costs are not offset by such adjustments when taking a shareholder perspective. We show that although we use a risk-neutral valuation framework based on a locally risk-free bank account, our final valuation equations do not depend on the risk-free rate. Finally, we show how to consistently derive a netting set valuation from a portfolio level one.
AU - Brigo,D
AU - Francischello,M
AU - Pallavicini,A
DO - 10.1016/j.ejor.2018.10.046
EP - 805
PY - 2019///
SN - 0377-2217
SP - 788
TI - Nonlinear valuation under credit, funding, and margins: existence, uniqueness, invariance, and disentanglement
T2 - European Journal of Operational Research
UR - http://dx.doi.org/10.1016/j.ejor.2018.10.046
UR - http://hdl.handle.net/10044/1/64598
VL - 274
ER -