TY - CPAPER
AB - We study conditions for existence, uniqueness and invariance of the comprehensivenonlinear valuation equations first introduced in Pallavicini et al (2011)[11]. These equations take the form of semi-linear PDEs and Forward-BackwardStochastic Differential Equations (FBSDEs). After summarizing the cash flows definitionsallowing us to extend valuation to credit risk and default closeout, includingcollateral margining with possible re-hypothecation, and treasury funding costs, weshow how such cash flows, when present-valued in an arbitrage free setting, leadto semi-linear PDEs or more generally to FBSDEs. We provide conditions for existenceand uniqueness of such solutions in a classical sense, discussing the role of thehedging strategy. We show an invariance theorem stating that even though we startfrom a risk-neutral valuation approach based on a locally risk-free bank accountgrowing at a risk-free rate, our final valuation equations do not depend on the riskfree rate. Indeed, our final semi-linear PDE or FBSDEs and their classical solutionsdepend only on contractual, market or treasury rates and we do not need to proxythe risk free rate with a real market rate, since it acts as an instrumental variable. Theequations derivations, their numerical solutions, the related XVA valuation adjustmentswith their overlap, and the invariance result had been analyzed numericallyand extended to central clearing and multiple discount curves in a number of previousworks, including [11], [12], [10], [6] and [4].
AU - Brigo,D
AU - Francischello,M
AU - Pallavicini,A
DO - 10.1007/978-3-319-33446-2_2
EP - 52
PB - Springer
PY - 2016///
SN - 2194-1009
SP - 37
TI - Analysis Of Nonlinear Valuation Equations Under Credit And Funding Effects
UR - http://dx.doi.org/10.1007/978-3-319-33446-2_2
UR - http://hdl.handle.net/10044/1/41720
ER -