A semi-static approach efficiently replicates and prices callable interest rate derivatives.
problem Efficiently replicating and pricing callable interest rate derivatives under dynamic market conditions.
method Proposes a semi-static hedging algorithm that updates the replication portfolio on a finite number of instances, rather than continuously.
result The hedging error can be made arbitrarily small with a sufficiently large replication portfolio, and closed-form error margins are determined.
The paper values perpetual callable American volatility options using a mean-reverting volatility model.
problem Valuation of callable American volatility put options.
method Modeling volatility dynamics as a mean-reverting 3/2 process and proposing a pricing formula.
result The value of perpetual callable American volatility put options is discussed under given conditions.
Study callable convertible bonds with liquidity constraints, generalizing previous work.
problem Callable convertible bond problem with liquidity constraints.
method Introduced a new technique to handle non-ordered payoff situations.
result Complete solution to callable convertible bond problem with liquidity constraint.
This paper addresses recalibration issues in hedging callable assets, proposing a new risk-adjusted approach.
problem The mismatch between dynamic hedging theory and practice due to daily recalibration.
method Extends HVA model risk approach to callable assets, focusing on recalibration and model risks.
result Model risk reserves adjusted for exercise decisions may significantly exceed basic valuation differences.
The paper compares machine learning methods with traditional techniques for pricing and sensitivities of financial products with path-dependent structures.
problem Evaluating financial products with early-termination clauses, especially those with path-dependent structures.
method The paper compares regression methods including randomized recurrent and feed-forward neural networks, and a novel approach using signatures of the underlying price process, with traditional polynomial basis functions for pricing and sensitivities.
result Machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates.
We develop a semi-analytic approach to the valuation of auto-callable structures with accrual features subject to barrier conditions. Our approach is based on recent studies of multi-assed binaries, present in the literature. We extend these studies to the case of time-dependent parameters. We compare numerically the s…
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonst…
We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and pu…
The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives with Libor market models is mainly carried out with Monte Carlo simulation. The PDE…
This paper improves SABR/LMM for better practical use in global banks.
problem Inflexibility of existing SABR/LMM models.
method Develops a comprehensive SABR/LMM model with time-dependent skew and smile.
result Provides a flexible and practical SABR/LMM model for global banks.
Paper proposes an analytical pricing model for puttable bonds with credit risk.
problem Analytical pricing of puttable bonds with credit risk.
method Developed a 2-factor structural PDE model and derived analytical pricing formula under specific conditions.
result Derived analytical pricing formula for puttable bonds with credit risk.
New method uses LSTM and signature theory to solve complex financial PDEs.
problem Solving path-dependent PDEs for financial derivatives pricing.
method Combining LSTM networks and rough paths theory.
result Efficient algorithms for pricing and hedging path-dependent derivatives.
New method prices interest rate derivatives without Monte Carlo, achieving high accuracy and speed.
problem Arbitrage-free pricing of path-dependent interest rate derivatives using infinite-dimensional models.
method Casting the stochastic pricing problem as a deterministic PDE solved by FINNs, which minimize violations of the PDE and boundary conditions.
result FINNs achieve pricing accuracy within 0.04 to 0.07 cents per dollar of contract value compared to Monte Carlo benchmarks.
Unified framework for pricing various debt securities.
problem Pricing of different types of debt securities under general short-rate processes.
method Unifying framework using continuous-time Markov chain approximations and bi-dimensional diffusion processes.
result Closed-form matrix expressions and efficient algorithms for pricing various debt securities.
We consider a two-factor model for the valuation of a non callable defaultable bond which pays coupons at certain given dates. The model under consideration is the Jump to Default Constant Elasticity of Variance (JDCEV) model. The JDCEV model is an improvement of the reduced form approach, which unifies credit and equi…
The paper proposes using function approximations to reduce the computational burden in measuring counterparty credit exposure.
problem The need for regular exposure calculations in finance, balancing between computational cost and risk simplification.
method Replacing derivative pricers with function approximations, proving error bounds, and using Chebyshev interpolation for convergence.
result Derives probabilistic and finite sample error bounds, showing significant run-time reductions and asymptotic efficiency gains.
New SL algorithms improve Bermudan Swaption pricing efficiency.
problem Efficient pricing of Bermudan Swaptions using Monte Carlo methods.
method Supervised Learning algorithms linking Bermudan Swaption to European Swaptions and other financial quantities.
result SL algorithms (Ridge, ANN, Gradient Boosted Regression Tree) are reliable and fast, overcoming Monte Carlo computational bottleneck.
QRAFTI uses multi-agent framework to improve equity factor research.
problem Replicating and developing new equity factors in large financial datasets.
method Integrates a research toolkit with MCP servers for data access and custom coding operations.
result Improves performance and explainability in multi-step empirical tasks.
In this paper we introduce a new algorithm for American Monte Carlo that can be used either for American-style options, callable structured products or for computing counterparty credit risk (e.g. CVA or PFE computation). Leveraging least squares regressions, the main novel feature of our algorithm is that it can be fu…
Improved Least-Squares Monte Carlo with finite-difference ansatz.
problem Improving accuracy and stability in option pricing.
method Constructing an ansatz using finite-difference solution for conditional expected continuation payoffs.
result Reduces mean squared error and final pricing error.
Paper solves bond option pricing with credit risk using Black-Scholes equations.
problem Pricing options on bonds with credit risk.
method Solution representations of Black-Scholes equations for specific problems.
result Pricing formulae for puttable and callable bonds with credit risk.
This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at fixed rate when the asset price is above a p…
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.
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.
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 …
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.