Develops a new model for cross-currency derivatives pricing.
problem Pricing cross-currency derivatives in a complex market model.
method Introduces a random field LIBOR market model to handle uncertainty in forward LIBOR rates.
result Derives exact and approximate pricing formulas for various derivatives.
Abstract framework for cross-currency interest rate contracts.
problem Handling cross-currency markets with collateral and incompleteness.
method Developed a general HJM framework for abstract market indices.
result Enabled simultaneous description of multiple currency interest rate products.
This paper examines pricing and hedging strategies for cross-currency equity protection swaps.
problem Dynamic requirements from EPS buyers in cross-currency equity protection swaps.
method Detailed analysis of two hedging paradigms, including separate and aggregated returns, with consideration of different types of returns.
result Proposes various hedging strategies with practical implications for EPS providers and investors.
Paper examines pricing and hedging for cross-currency swaps referencing backward-looking rates.
problem Pricing and hedging cross-currency swaps with backward-looking rates.
method Uses interest rate and currency futures for hedging, analyzes arbitrage-free multi-curve setting.
result Explicit pricing and hedging results for CCBS with backward-looking rates.
Model shows triangular arbitrage key to cross-currency correlations in forex markets.
problem Understanding cross-currency correlations in forex markets.
method Agent-based model of market interactions.
result Triangular arbitrage is primary driver of cross-currency correlations.
Transformer predicts Ethereum prices using cross-currency correlation and sentiment analysis.
problem Predicting Ethereum cryptocurrency prices with limited data.
method Transformer-based neural network with cross-currency correlation and sentiment analysis.
result Transformer model outperforms other models on some parameters.
Proposes a new method to assess Wrong-Way Risk in cross-currency swaps.
problem Addressing Wrong-Way Risk (WWR) in cross-currency swaps with stochastic correlation modeling.
method Proposes a stochastic correlation approach to model the dependency between exposure and counterparty credit risk, capturing tail dependence.
result The impact of stochastic correlation on calculated CVA is substantial, providing a promising method to model WWR.
This research uses empirical copulas to price quanto options, showing significant differences from traditional models.
problem The dependence relation between currency and asset prices affects quanto option pricing.
method Empirical copulas are used to model the dependence between currency and asset prices.
result Empirical copulas provide non-negligible pricing differences compared to traditional models.
The financial crisis of 2007/08 caused catastrophic consequences and brought a bunch of changes around the world. Interest rates that were known to follow or behave similarly of each other diverged. Furthermore, the regulation and in particular the counterparty credit risk began to to be considered and quantified. Cons…
We present a general derivation of the arbitrage-free pricing framework for multiple-currency collateralized products. We include the impact on option pricing of the policy adopted to fund in foreign currency, so that we are able to price contracts with cash flows and/or collateral accounts expressed in foreign currenc…
Study proposes a method to construct copulas using corrected Hermite polynomial expansion for estimating foreign exchange volatility.
problem Estimating cross foreign exchange volatility with complex correlation structures.
method Applying corrections to the finite sum of multivariate Hermite polynomial expansions to construct copulas.
result The proposed copula method accurately reproduces the volatility smile of cross currency pairs.
We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market…
Study multi-currency markets with multiple interest rates and collateral.
problem Characterize absence of arbitrage in a multi-currency market.
method Generalize results from Bielecki and Rutkowski (2015) to a multi-currency framework, linking with Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). Characterize absence of arbitrage without collateral, then study collateralization schemes under various conventions.
result Complete study of absence of arbitrage and pricing in multi-currency markets with multiple interest rates and collateral.
In the forthcoming ISDA Standard Credit Support Annex (SCSA), the trades denominated in non-G5 currencies as well as those include multiple currencies are expected to be allocated to the USD silo, where the contracts are collateralized by USD cash, or a different currency with an appropriate interest rate overlay to ac…
Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts. This work gives its extension r…
A new challenge to quantitative finance after the recent financial crisis is the study of credit valuation adjustment (CVA), which requires modeling of the future values of a portfolio. In this paper, following recent work in [Weinan E(2017), Han(2017)], we apply deep learning to attack this problem. The future values …
It is well known that traded foreign exchange forwards and cross currency swaps (CCS) cannot be priced applying overnight cash and carry arguments as they imply absence of funding advantage of one currency to the other. This paper proposes a heuristic present value concept for multi-currency pricing and hedging which a…
A method to complete incomplete correlation matrices using maximum entropy.
problem Incomplete correlation matrices in financial applications.
method Maximizing entropy of the distribution described by the matrix, constructing a chordal graph.
result A proper correlation matrix can be constructed for large models involving multiple currencies.
The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of paths for nested Monte Carlo simulations, resulting in large variances of estimator…
The Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between…
Researchers found the Wigner derivative and its inverse are equal for spherical tetrahedra.
problem Computing the relationship between dihedral angles and edge lengths in tetrahedra.
method Computed the Wigner derivative and its inverse for spherical tetrahedra.
result The Wigner derivative and its inverse are equal for spherical tetrahedra.
The paper shows objective derivatives are covariant derivatives on Riemannian metrics.
problem The definition and interpretation of objective derivatives in continuum mechanics.
method Demonstrates that objective derivatives correspond to covariant derivatives on the manifold of Riemannian metrics.
result Objective derivatives are unified as covariant derivatives on the manifold of Riemannian metrics.
Computes derivatives of sections in vector bundles using Lie derivatives.
problem Computing time derivatives of sections in natural vector bundles.
method Extending a lemma to compute Lie derivatives of sections of natural vector bundles.
result Computed derivatives of sections in vector bundles using Lie derivatives.
Paper proposes auction method for smart derivatives to avoid disputes.
problem Disputes over derivative liquidation processes in smart contracts.
method Defines an auction type resolution for smart derivatives.
result Proposes a beneficial method for smart derivatives participants.
Derivatives impact U.S. banking sector's systemic risk, but loan and leverage ratios are more significant.
problem Systemic risk in U.S. banking sector due to derivatives and loans.
method Analysis of derivatives and loan data to assess systemic risk.
result Loan and leverage ratios are more influential in systemic risk than derivatives holdings.
This paper deals with the concept of curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving a closed form formula to obtain any order derivative of the curvature tensor as …
Schwarzian derivative connects to Euler-Lagrange equations in variational calculus.
problem Understanding the relationship between the Schwarzian derivative and variational equations.
method Analyzing the Schwarzian derivative as a first integral and Euler-Lagrange operator for specific variations.
result The Schwarzian derivative is both a first integral and the Euler-Lagrange operator for a certain class of variations.
Paper develops formulas for shape derivatives in wave scattering.
problem Computing high order shape derivatives for wave scattering is challenging.
method Introduces elegant recurrence formulas using differential forms and Lie derivatives.
result Unified framework for computing high order shape perturbations in scattering problems.
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
Study compares Indian derivatives markets and finds NSE outperforming BSE.
problem Lack of strong regulations and robust framework in Indian derivatives market.
method Comparison of performance of derivatives in BSE and NSE, analysis of derivatives with cash market and market volatility.
result NSE derivatives outperform BSE, need stronger regulations.
Former physicists share insights on derivatives in interviews.
problem Understanding physics in finance interview questions.
method Interviews with former physicists in finance.
result Compilation of physics-related interview answers.
Introduces Darboux-Lie derivative for fiber bundles.
problem None explicitly stated; focuses on introducing a new derivative.
method Study of Darboux-Lie derivative for fiber-bundle maps.
result Properties of Darboux-Lie derivative for fiber bundles.
New derivations on diffeological spaces are not smooth, expanding tangent space definitions.
problem Lack of smoothness in derivations on diffeological spaces.
method Examined derivations satisfying the Leibniz rule but not smooth with respect to given diffeology.
result Tangent space defined via all derivations is larger than one defined using only smooth derivations.
Develops derived differential geometry theory.
problem Homotopy and intersection in smooth manifolds.
method Using L∞[1]-algebras and homotopy transfer. result Derived manifolds form a category of fibrant objects.
Derives spacetime regularity under specific curvature conditions.
problem Ensuring smoothness in spacetime models with given curvature constraints.
method General regularity estimate for 4-d spacetimes, using Ricci curvature and Lie derivatives.
result Establishes conditions for smoothness in spacetime models.
In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation …
Approximates derivative pricing under fractional stochastic volatility.
problem Derivative pricing under fractional stochastic volatility model.
method Approximate expression derived from deterministic functions and fractional Ornstein-Uhlenbeck process.
result Numerical simulations show the feasibility and effect of long-range dependencies on derivative prices.
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier work. Examples of higher derived brackets naturally appear in geometry and mathem…
We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…
We calculate the higher derivatives of length functions on Teichmuller space along earthquake deformations. This generalizes the cosine formula for the first derivative by Kerckhoff and Wolpert and the sine formula for second derivative by Wolpert.
Develops a new approach to study nonlinear PDEs and their singularities.
problem Understanding the propagation domains of solutions to nonlinear PDEs.
method Derived geometric machinery and sheaf theory to study nonlinear PDEs and their singular supports.
result Estimates the domains of propagation for solutions of non-linear systems.
Derives derivatives of risk measures for various types of portfolio losses.
problem Calculating precise risk measures for portfolio losses.
method Analyzes first and second order derivatives of risk measures for both continuous and discrete portfolio loss scenarios.
result Provides asymptotic results for conditional moments of heavy-tailed portfolio losses.
Optimizes material distribution on surfaces using topological derivatives.
problem Optimal distribution of two materials on smooth submanifolds in Rd. method Topological derivative approach for shape optimization constrained by PDEs.
result Numerical solution of topology optimization problem on surfaces.
Derives a formula for the k-th covariant derivative of tensor fields.
problem Finding a formula for the k-th covariant derivative of tensor fields.
method Introducing symbols P and Q depending on Christoffel symbols, deriving a formula (3.1).
result Derives a formula for the k-th covariant derivative of tensor fields.
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…
Invariant covariant derivatives on homogeneous spaces are characterized.
problem Understanding invariant covariant derivatives on homogeneous spaces.
method Expressing covariant derivatives in terms of horizontally lifted vector fields and bilinear maps.
result Existence and characterization of invariant covariant derivatives.
Derives derivatives and geometric framework for functions with non-independent variables.
problem Characterizing functions with non-independent variables in probabilistic models.
method Derives actual and dependent partial derivatives, dependent Jacobian matrix, and tensor metric.
result Derives gradient, Hessian, and Taylor expansion for functions with non-independent variables.
We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and include existence and classification of various deformation quantisations.