This paper addresses credit valuation adjustment with a new closeout convention.
problem Accurate estimation of financial claim value considering counterparty credit risk.
method Theoretical and computational analysis of a nonlinear valuation system using neural networks.
result A neural network-based algorithm effectively solves the high-dimensional nonlinear valuation system.
Study on nonlinear valuation equations for credit risk, collateral, and funding costs, proving existence, uniqueness, and invariance.
problem Nonlinear valuation equations for credit risk, collateral, and funding costs.
method Analyzes conditions for existence, uniqueness, and invariance of nonlinear valuation equations, including PDEs and FBSDEs.
result Existence and uniqueness of solutions for nonlinear valuation equations, with invariance of the final equations to the risk-free rate.
Framework for robust credit risk valuation adjustments.
problem Valuation of credit default swap portfolios with uncertain counterparty bond returns.
method Arbitrage-free framework, bounds derived from nonlinear ODEs, collateral and closeout payoffs considered.
result Upper and lower bounds for XVA process derived, showing nonlinear effects of credit contagion.
Extends pricing of American options in nonlinear markets.
problem Pricing American options in nonlinear markets.
method Detailed study of unilateral valuation problems, BSDE approach.
result Explicit pricing, hedging, and exercising results.
The paper explores optimal investment and contingent claim valuation in illiquid markets using convex duality.
problem Optimal investment and contingent claim valuation in markets with nonlinear trading costs and portfolio constraints.
method Convex duality theory applied to markets with general conditions on utility functions and market models.
result Dual expressions decompose into terms for risk preferences, trading costs, and portfolio constraints.
The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach fo…
The paper deals with incorporating statistical uncertainty in decision-making.
problem Statistical uncertainty in decision-making.
method Theory of nonlinear expectations.
result Explicit and consistent incorporation of uncertainty in decision valuation.
The paper develops a comprehensive valuation method for OTC claims that considers credit and funding risks.
problem Valuation of Over-The-Counter (OTC) claims that incorporate credit and funding liquidity risks.
method Develops a holistic approach using nonlinear mathematical models (semilinear PDEs and FBSDEs) and provides an analytical solution for the benchmark claim.
result An analytical solution for the benchmark claim is derived and expressed in terms of the Black-Scholes formula with dividends.
The research presented in this work is motivated by recent papers by Brigo et al. (2011), Burgard and Kjaer (2009), Crépey (2012), Fujii and Takahashi (2010), Piterbarg (2010) and Pallavicini et al. (2012). Our goal is to provide a sound theoretical underpinning for some results presented in these papers by developing …
We propose a discrete time algorithm for the valuation of employee stock options based on exponential indifference prices and taking into account both the possibility of partial exercise of a fraction of the options and the use of a correlated traded asset to hedge part of their risk. We determine the optimal exercise …
Fast ML framework for derivative valuation from volatility surfaces.
problem Derivative valuation from complex volatility surfaces.
method Parameterized SVI model, synthetic market scenarios, Gaussian Process Regressor.
result Very accurate and fast (3-4 orders of magnitude) derivative valuations.
CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?q-fin.PR We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed…
Develops a new option pricing model under G-expectation framework.
problem Modeling uncertainty in financial markets and robust valuation under model uncertainty.
method G-expectation framework, logarithmic transformation, finite difference schemes.
result Unified risk-neutral valuation approach yielding G-Black-Scholes equation.
Study analyzes Nifty 50 returns over 34 years, showing P/E ratio predicts long-term gains.
problem Understanding equity return dynamics in the Indian market over various horizons.
method Unified, distribution-aware, complexity-informed framework using 34 years of Nifty 50 data.
result P/E ratio probabilistically maps return distributions across different investment horizons.
Machine learning improves beta forecasts, enhancing equity valuation and portfolio performance.
problem Improving beta forecasts for better equity valuation and portfolio performance.
method Using machine learning on a large cross-section of US stocks with various firm characteristics.
result Machine learning improves out-of-sample performance of asymmetric beta measures.
We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a general pricing equation whe…
New method uses Hermite polynomials for American option valuation.
problem Valuation of American options with complex jump-diffusion dynamics.
method Hermite polynomial expansions of transition density and early exercise premium.
result Converging approximations to true option prices and exercise boundaries.
Researchers derive a formula for Brownian motion transition probability in a specific octant.
problem Computing default probabilities and credit valuation adjustments in structural credit models.
method Semi-analytic formula derived using separation of variables in spherical coordinates, followed by numerical methods to solve the resulting eigenvalue problem.
result A solution to the transition probability problem expressed as an expansion into special functions and an eigenvalue.
Paper introduces new actuarial-consistent valuations for insurance liabilities.
problem Valuation of insurance liabilities considering both financial and actuarial risks.
method Proposes two-step actuarial valuations and actuarial-consistent procedures.
result Actuarial-consistent valuations are equivalent to two-step actuarial valuations under coherence.
Climate-Dyna learns residual climate HVA for XVAs using model-based RL.
problem Tackles residual climate HVA in XVAs not inferred from stand-alone stress loss.
method Combines residual climate HVA with model-based reinforcement learning.
result Reduces climate charge from 1.517 to 0.831 in EU ETS study.
Paper recovers uncertainty from dynamic valuation rules.
problem Recovering latent uncertainty from observable valuation rules.
method Developed procedures to identify and characterize uncertainty structures from valuation rules.
result Valuation rules contain sufficient information to identify and recover uncertainty structures.
Study convolution of invariant valuations on Lie groups.
problem Understanding convolution of valuations on Lie groups.
method Explicit formula for left-invariant valuations, showing existence of smooth bi-invariant valuations, defining convolution on arbitrary Lie groups.
result Unified convolution operations on Lie groups.
Complete description of valuations for indefinite orthogonal groups.
problem Classifying valuations for indefinite orthogonal groups.
method Detailed analysis of continuous and generalized translation- and group-invariant valuations.
result Identification of Klain-Schneider continuous valuations within the space of translation-invariant valuations.
SL(n) covariant valuations on Orlicz spaces are represented and characterized.
problem Representing SL(n) covariant valuations on Orlicz spaces.
method Representation theorem established for continuous, SL(n) covariant vector-valued valuations.
result Unique characterization of SL(n) covariant valuations as moment vectors.
Paper explains accrual and mark-to-market valuation for interest rate trades.
problem Understanding the valuation differences between accrual and mark-to-market methods for interest rate trades.
method Comparison of discounted cashflow valuation to spread-based valuation, Taylor series approximation, and deferral concept.
result Simple intuition and mathematical explanation of accrual and mark-to-market adjustments.
Market valuation duration is 175 years, but drops to 46 years during crises.
problem Understanding the duration of market valuation and its impact on returns.
method Comparing market valuation ratios and dividends to estimate duration, analyzing the discount rate effect.
result Valuation duration is negatively correlated with market returns, with a robust out-of-sample R2 of 15%.
Paper simplifies default process modeling and credit valuation.
problem Modeling and pricing derivative securities with credit risk.
method Integrates default process, probability, and correlation into a unified framework.
result Risky valuation is Martingale in the proposed model.
Introduces convolution of valuations on manifolds and groups.
problem Defining and studying convolution of valuations on manifolds and groups.
method Introduces new notion of convolution, proves it as a module over compactly supported generalized valuations, and provides explicit formulas.
result Convolution is an extension of smooth translation invariant valuations on manifolds.
Business cycles affect startup valuations, both directly and indirectly.
problem How do business cycles impact startup valuations?
method Structural Equation Model approach using a dataset of 1,089 venture capital investments.
result Business cycles impact startup valuations both directly and indirectly.
Classification of SL(n) covariant valuations on Orlicz spaces.
problem Classifying continuous SL(n) covariant valuations on Orlicz spaces.
method Complete classification without symmetric assumptions, focusing on moment matrix and a new functional in dimension two.
result The moment matrix is the only SL(n) covariant valuation for n≥3, and a new functional appears in dimension two.
New method solves high-dimensional PDEs and 2BSDEs efficiently.
problem High-dimensional fully nonlinear PDEs and 2BSDEs in financial models.
method Connection between PDEs and 2BSDEs, merged formulation, temporal discretization, spatial approximation via neural nets, stochastic gradient descent.
result Efficient and accurate solution for high-dimensional nonlinear expectations.
We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achie…
Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.
problem Classifying contravariant matrix-valued valuations on polytopes without continuity assumptions.
method Complete classification of contravariant matrix-valued valuations on polytopes in Rn without continuity assumptions. result The only such valuation is the general Lutwak-Yang-Zhang matrix in dimension n≥4, and a new function in dimension 3. Paper proposes a new method for valuing long-term annuities using real-world probability measure.
problem Valuation of long-term annuities using classical no-arbitrage methods.
method Real-world probability measure valuation, employing numéraire portfolio.
result Real-world valuation leads to lower values than classical approaches.
Study evaluates valuation models for UK companies using case studies.
problem Determining how accounting numbers affect business value.
method Comprehensive review of three valuation models: FCFVM, REVM, AEGM.
result Accounting numbers through valuation models can affect business value.
Models value assets based on non-devaluation, creating global valuation formulas.
problem Valuation of assets that can potentially lose value.
method Conditioning on non-devaluation, using each asset as a numéraire, and aggregating local valuation rules.
result Global arbitrage-free valuation formulas can be derived from local rules.
The paper extends the convolution operator to non-smooth valuations using geometric inequalities.
problem Extending the convolution operator to non-smooth valuations.
method Using geometric inequalities derived from optimal transport methods.
result Constructing a continuous extension of the convolution operator on smooth valuations to non-smooth valuations.
The classification of continuous, translation invariant Minkowski valuations which are contravariant (or covariant) with respect to the complex special linear group is established in a 2-dimensional complex vector space. Every such valuation is given by the sum of a valuation of degree of homogeneity 1 and 3. In dimens…
Computes tube formulas for valuations in complex space forms.
problem Computing values of valuations on complex space forms.
method Develops tube formulas for valuations in complex space forms and generalizes classical formulas.
result Generalizes classical formulas of Weyl, Gray and others.
Study kinematic formulas for quaternionic plane valuations.
problem Kinematic formulas for quaternionic plane valuations.
method Introduced different bases and determined kinematic formulas.
result Complete set of kinematic formulas for quaternionic plane valuations.
Value-tracking in financial markets breaks down when non-valuation-based traders dominate.
problem Understanding the threshold for value-tracking in financial markets.
method Simple discrete-time model to show how non-valuation-based traders can cause tracking errors.
result A threshold above which value-tracking breaks down without changes in asset value.
Existence of smooth valuations on subspaces is shown for certain conditions.
problem Existence of smooth valuations on subspaces with given restrictions.
method Analyzing compatibility and using recursive descriptions of the cosine transform.
result Compatibility is sufficient for extensibility in certain regimes.
Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.
problem Classifying SL(n) covariant matrix-valued valuations on Lp-spaces.
method Established a complete classification for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx), eliminating matrix symmetry assumption.
result Unique characterization of such valuations by the moment matrix in n>2, rotation matrix in 2D.
Develops a new method to study algebraic tangent cones of sheaves using valuations.
problem Analyzing tangent cones of torsion-free sheaves on algebraic varieties.
method Introduces a slope stability theory and uses it to define a canonical tangent cone for quasi-regular valuations.
result Shows the existence of a canonical tangent cone for torsion-free sheaves, up to equivalence.
Derives valuations for financial portfolios from securities lending perspective.
problem Valuation of financial portfolios from securities lending perspective.
method Derives valuations under different assumptions and shows a weighting scheme.
result Weighting scheme converges faster to true valuation under certain conditions.
Fair market valuations ignore future worker profits in employee-owned firms.
problem Ignoring future worker profits in fair market valuations for employee-owned firms.
method Analyzing property rights and residual claimants in employee-owned firms.
result Fair market valuations are inappropriate for employee-owned firms.
We study the properties of the multiplicative structure on valuations on convex sets. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss related problems of integral geometry. Then we formulate a conjectural analogue of this result for odd valuations.
We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.