Mild to classical solutions for XVA equations under stochastic volatility

DOI10.1137/22M1506882MaRDI QIDQ6496950

Damiano Brigo, Federico Graceffa, A. V. Kalinin

Publication date: 6 May 2024

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

zbMATH Keywords

collateralstochastic differential equationstochastic volatilitymild solutionvaluationdefault timesemilinear parabolic PDEfunding costsXVA

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20) Semilinear parabolic equations (35K58)

Cites Work

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• The Pricing of Options and Corporate Liabilities
• Counterparty risk and funding: immersion and beyond
• Classical solutions to reaction-diffusion systems for hedging problems with interacting Itô and point processes
• On changes of measure in stochastic volatility models
• Nonlinear valuation under credit, funding, and margins: existence, uniqueness, invariance, and disentanglement
• Path-dependent equations and viscosity solutions in infinite dimension
• Markovian integral equations
• On the support of solutions to stochastic differential equations with path-dependent coefficients
• BSDEs of counterparty risk
• A change-of-variable formula with local time on curves
• Multidimensional diffusion processes.
• Backward Stochastic Differential Equations in Finance
• Arbitrage‐free XVA
• Analysis of Nonlinear Valuation Equations Under Credit and Funding Effects
• When Capital Is a Funding Source: The Anticipated Backward Stochastic Differential Equations of X-Value Adjustments
• A Unified Approach to xVA with CSA Discounting and Initial Margin
• COLLATERALIZED CVA VALUATION WITH RATING TRIGGERS AND CREDIT MIGRATIONS
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• ARBITRAGE‐FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS
• Counterparty Credit Risk, Collateral and Funding
• Measure and integration theory. Transl. from the German by Robert B. Burckel

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