Imperial College London

ProfessorDamianoBrigo

Faculty of Natural SciencesDepartment of Mathematics

Chair in Mathematical Finance
 
 
 
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Contact

 

damiano.brigo

 
 
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Location

 

805Weeks BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Brigo:2015,
author = {Brigo, D and Francischello, M and Pallavicini, A},
title = {Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs},
url = {http://arxiv.org/abs/1506.00686v2},
year = {2015}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - We study conditions for existence, uniqueness and invariance of thecomprehensive nonlinear valuation equations first introduced in Pallavicini etal (2011). These equations take the form of semilinear PDEs andForward-Backward Stochastic Differential Equations (FBSDEs). After summarizingthe cash flows definitions allowing us to extend valuation to credit risk anddefault closeout, including collateral margining with possiblere-hypothecation, and treasury funding costs, we show how such cash flows, whenpresent-valued in an arbitrage free setting, lead to semi-linear PDEs or moregenerally to FBSDEs. We provide conditions for existence and uniqueness of suchsolutions in a viscosity and classical sense, discussing the role of thehedging strategy. We show an invariance theorem stating that even though westart from a risk-neutral valuation approach based on a locally risk-free bankaccount growing at a risk-free rate, our final valuation equations do notdepend on the risk free rate. Indeed, our final semilinear PDE or FBSDEs andtheir classical or viscosity solutions depend only on contractual, market ortreasury rates and we do not need to proxy the risk free rate with a realmarket rate, since it acts as an instrumental variable. The equationsderivations, their numerical solutions, the related XVA valuation adjustmentswith their overlap, and the invariance result had been analyzed numerically andextended to central clearing and multiple discount curves in a number ofprevious works, including Pallavicini et al (2011), Pallavicini et al (2012),Brigo et al (2013), Brigo and Pallavicini (2014), and Brigo et al (2014).
AU - Brigo,D
AU - Francischello,M
AU - Pallavicini,A
PY - 2015///
TI - Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs
UR - http://arxiv.org/abs/1506.00686v2
ER -