This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-consistency properties for a firm seeking to spread its risk across a group of subsidiaries.
We develop a novel stochastic valuation and premium calculation principle based on probability measure distortions that are induced by quantile processes in continuous time. Necessary and sufficient conditions are derived under which the quantile processes satisfy first- and second-order stochastic dominance. The introduced valuation principle relies on stochastic ordering so that the valuation risk-loading, and thus risk premiums, generated by the measure distortion is an ordered parametric family. The quantile processes are generated by a composite map consisting of a distribution and a quan…
The Recalibration Conundrum: Hedging Valuation Adjustment for Callable Claims
Université Paris-Saclay, CNRS, Univ Evry, ensIIE, Laboratoire de Mathématiques et Modélisation d’Evry（巴黎萨克雷大学，法国国家科学研究中心，埃夫里大学，ensIIE，埃夫里数学与建模实验室）；Université Paris Cité, Laboratoire de Probabilités, Statistique et Modélisation (LPSM), CNRS UMR 8001（巴黎西岱大学，概率、统计与建模实验室（LPSM），法国国家科学研究中心 UMR 8001）
In March 2020, the world was thrown into financial distress. This manifested itself in increased uncertainty in the financial markets. Many interest rates collapsed, and funding spreads surged significantly, which increased due to the market turmoil. In light of these events, it is essential to understand and model Wrong-Way Risk (WWR) in a Funding Valuation Adjustment (FVA) context. WWR may currently be absent from FVA calculations in banks' Valuation Adjustment (xVA) engines. However, in this letter, we demonstrate that WWR effects are non-negligible in FVA modelling from a risk-management p…
Valuation of Variable Annuities with Equity Protection Swaps under Jumps and Default Risks
School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学院）；Faculty of Mathematics and Information Science, Warsaw University of Technology（华沙理工大学数学与信息科学学院）；National University of Singapore, Department of Mathematics（新加坡国立大学数学系）
While abundant empirical studies support the long-range dependence (LRD) of mortality rates, the corresponding impact on mortality securities are largely unknown due to the lack of appropriate tractable models for valuation and risk management purposes. We propose a novel class of Volterra mortality models that incorporate LRD into the actuarial valuation, retain tractability, and are consistent with the existing continuous-time affine mortality models. We derive the survival probability in closed-form solution by taking into account of the historical health records. The flexibility and tracta…
This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a $σ$-subalgebra and a degree of model uncertainty. When the random vector represents the payoff of derivative security in a complete financial market, its R-conditioning with respect to the risk-neutral measure is interpreted as its risk-averse value. The optimization problem defining the optimization R-conditioning is shown to be well-posed. We show that the R-conditionin…
We introduce a general model for the balance-sheet consistent valuation of interbank claims within an interconnected financial system. Our model represents an extension of clearing models of interdependent liabilities to account for the presence of uncertainty on banks' external assets. At the same time, it also provides a natural extension of classic structural credit risk models to the case of an interconnected system. We characterize the existence and uniqueness of a valuation that maximises individual and total equity values for all banks. We apply our model to the assessment of systemic r…
We introduce a neural network approach for assessing the risk of a portfolio of assets and liabilities over a given time period. This requires a conditional valuation of the portfolio given the state of the world at a later time, a problem that is particularly challenging if the portfolio contains structured products or complex insurance contracts which do not admit closed form valuation formulas. We illustrate the method on different examples from banking and insurance. We focus on value-at-risk and expected shortfall, but the approach also works for other risk measures.
This paper investigates calculations of robust XVA, in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA) for over-the-counter derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk and funding risk can be characterized (and indeed quantified) via the robust XVA formulations. The simpler dual formulations are derived using recent infinite dimensional Lagrangian duality results. Next, some computational experiments are conducted to measure the additional XVA charges due to distributio…
