Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional finite difference solutions,…
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48 results for “finite-difference method”
We evaluate the hedging performance of a high-order compact finite difference scheme from [4] for option pricing in Bates model. We compare the scheme's hedging performance to standard finite difference methods in different examples. We observe that the new scheme outperforms a standard, second-order central finite dif…
New method for pricing options in stochastic volatility models.
problem Pricing options in models with stochastic volatility.
method Time-adaptive, high-order compact finite difference scheme.
result Extends fourth-order multistep methods to stochastic volatility models.
This study reveals efficient finite-difference computation for gradient regularization in deep learning.
problem Improving generalization performance in deep learning through gradient regularization.
method Analyzes and reveals a specific finite-difference computation that reduces computational cost and improves generalization performance.
result Finite-difference computation strengthens the implicit bias towards rich regimes and enhances generalization performance.
The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.
problem Estimating gradients of smooth functions using noisy function evaluations.
method Information-theoretic lower bounds and finite difference method analysis.
result The finite difference method is not minimax optimal, suggesting room for improvement in gradient estimation.
High-order compact finite difference scheme for option pricing in stochastic volatility jump modelsq-fin.CP
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in ti…
Instabilities of explicit finite difference schemes with ghost points on the diffusion equationmath.NA
Ghost points affect stability in finite difference schemes for diffusion equations.
problem Impact of ghost points on stability of finite difference schemes.
method Exploration of explicit Euler finite difference scheme with ghost points on diffusion equation.
result Stability of the scheme is affected by ghost points.
Paper applies subdiffusive dynamics to American and barrier options pricing.
problem Valuation of American and barrier options in subdiffusive financial models.
method Proposes weighted finite difference and Longstaff-Schwartz methods for valuation.
result Numerical valuation of American and barrier options demonstrated.
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original function's finite differences.
We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the rel…
There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to ca…
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
problem Improving option pricing accuracy in volatile financial markets.
method Extended Black-Scholes model using finite difference method and LSTM machine learning.
result Finite difference method outperforms LSTM in computational efficiency but not in accuracy.
We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Lévy semistationary (LSS) processes, which is a class of processes that have been…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In pro…
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
problem Accurate hedging strategies in dynamic market environments.
method Asymptotic approach and finite difference techniques.
result Reduction of hedge errors and enhancement of option pricing model robustness.
FD-Net with Auxiliary Time Steps: Fast Prediction of PDEs using Hessian-Free Trust-Region Methodscs.LG
FD-Net predicts future dynamics from data using Hessian-Free TRCG method.
problem Discovering hidden partial differential equations from data.
method Finite-difference inspired convolutional neural network with Hessian-Free TRCG method.
result FD-Net predicts future dynamics efficiently using few trainable parameters.
Paper optimizes aquaculture feeding and harvesting strategies for profit maximization.
problem Maximizing farm profit through optimal feeding and harvesting decisions under stochastic price dynamics.
method Developed a simplified aquaculture model and two numerical solution approaches: finite difference scheme and PINN-based method combined with DeepOS algorithm.
result PINN-based method achieves comparable accuracy to finite differences but is more scalable.
Algorithm solves American options with regime-switching using multigrid and compact finite difference.
problem Pricing American put options with regime-switching.
method Multigrid iterative algorithm based on compact finite difference schemes and Hermite interpolation.
result The algorithm provides a fast and efficient tool for pricing American put options with regime-switching.
FDNet learns PDEs from data with fast predictions.
problem Discovering complex systems behavior from data.
method Finite difference neural networks (FDNet) to learn PDEs from trajectory data.
result FDNet predicts future behavior with few trainable parameters.
A new method for pricing options with stochastic volatility and jumps.
problem Pricing options under stochastic volatility and jumps.
method Fourth-order compact finite-difference scheme with implicit-explicit Crank-Nicolson framework.
result The method achieves near-fourth-order spatial accuracy and up to two orders of magnitude lower runtime than quadratic finite elements.
Credit value adjustment (CVA) is the charge applied by financial institutions to the counterparty to cover the risk of losses on a counterpart default event. In this paper we estimate such a premium under the Bates stochastic model (Bates [4]), which considers an underlying affected by both stochastic volatility and ra…
New method uses adaptive sampling for optimization in uncertain conditions.
problem Optimizing functions with unknown gradients in uncertain environments.
method Adaptive sampling quasi-Newton method with finite differences and norm tests.
result Potential performance benefits of the proposed method demonstrated in preliminary experiments.
A discrete method approximates hyperbolic curvature flow in the plane.
problem Modeling wave phenomena in solid-liquid interfaces.
method Semidiscrete finite difference method for hyperbolic curvature flow.
result Error bounds for natural discrete norms are proven.
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme being a generalizat…
The paper compares inserting and stretching points for grid refinement near critical points.
problem Decreased accuracy of finite difference methods near discontinuities.
method Comparison of inserting and stretching points for grid refinement near critical points.
result Proposes a new fast and simple stretching function.
Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's …
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.
Quantum computing speeds up pricing multi-asset derivatives.
problem Exponential growth in complexity for multi-asset derivatives pricing.
method Quantum algorithm based on quantum linear system algorithms for FDM.
result Exponential speedup in derivative pricing compared to classical methods.
A pairs trading model with time-varying volatility using stochastic control.
problem Optimizing pairs trading strategies with fluctuating asset volatilities.
method Stochastic control techniques, Finite Difference method, Generalized Method of Moments.
result Optimal trading strategies maximizing expected power utility from terminal wealth.
Optimal reinsurance strategies for multi-line insurance companies.
problem Choosing the best dynamic reinsurance policies for multi-line insurance companies.
method Characterized the optimal survival function as the unique nondecreasing viscosity solution of the HJB equation, solved numerically using the finite difference method.
result Provided proof of convergence of numerical solution to the survival probability function.
Efficiently approximates higher-order derivatives for generative models.
problem Expensive computation of higher-order derivatives in generative models.
method Rewrite SM objective in terms of directional derivatives and use finite difference for efficient approximation.
result Comparable results to gradient-based methods but significantly more computationally efficient.
Pricing Derivatives under Self-Exciting Dynamics: A Finite-Difference and Transform Approachq-fin.MF
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
A new method for computing Greeks without bias, improving stability.
problem Inaccurate and unstable computation of second order Greeks (like Gamma) in financial instruments.
method Apply Chebyshev interpolation techniques to finite differences for improved stability.
result Improved stability and accuracy in computing spot Greeks without bias.
Enhanced DFO using adaptive batch-based FD estimates.
problem Derivative-free optimization with imprecise gradient estimates.
method Adaptive batch-based finite difference estimation and dynamic sampling strategy.
result Algorithm achieves convergence rate similar to KW and SPSA methods.
Neural network solves BVPs with unstructured data.
problem Solving Boundary Value Problems (BVPs) with numerical methods.
method Neural Network based numerical method for solving BVPs.
result Validated the method for Laplace and Poisson equations.
Study evaluates and compares numerical differentiation methods on three case studies.
problem Evaluating and comparing numerical differentiation methods for efficiency.
method Forward, Backward, and Centered Finite-Difference methods applied at two levels of precision.
result Different methods perform differently across case studies, with varying levels of computational cost and accuracy.
Unified framework for Arnold-type invariants via dual complexes and finite-difference structures.
problem Study of Arnold-type invariants of immersed curves and surfaces.
method Framework on dual complexes, locally normalized maps, finite-difference structures, and Shumakovitch-type identities.
result Unified evaluation of Arnold-type invariants and on dual skeleta.
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…
Finite element method applied to Leland's model for option pricing with transaction costs.
problem Option pricing with transaction costs using Leland's model.
method Spatial finite element models based on P1 and/or P2 elements combined with a Crank-Nicolson-type temporal scheme.
result Results compare favorably with finite difference methods in the literature.
This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations are consistent. This approach is partly inspired by Andreasen & Huge, 2011 who re…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic sp…
ES and FD gradients converge as optimization dimension grows.
problem Understanding the relationship between Evolution Strategies and Finite Differences gradients.
method Analyzing the convergence of gradients as the optimization dimension increases.
result ES and FD gradients converge as the dimension of the vector under optimization increases.
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfull…
A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal withdrawal strategy of a policyholder,…
Study non-perturbative quantum geometry of string theories using finite difference equations and resurgence analysis.
problem Non-perturbative quantum geometry of open and closed topological string on the resolved conifold.
method Finite difference equations, resurgence analysis, exact WKB techniques.
result Identify 5d BPS states and relate spectral problems to quantum integrable systems.
Effective dimensionality reduction improves accuracy and reduces costs in estimating option Greeks.
problem Estimating Greeks for barrier and arithmetic average Asian options.
method Global sensitivity analysis, Chebyshev interpolation, conditional pathwise method, randomized Quasi Monte Carlo, Brownian bridge discretization, importance sampling.
result Reduced effective dimensionality enhances convergence rate and accuracy of randomized Quasi Monte Carlo integration.
Flexible framework for optimal trading across multiple asset venues.
problem Optimal trading in assets listed on different venues considering liquidity dependencies.
method Bayesian update of model parameters, finite difference method, deep reinforcement learning.
result Adaptive trading strategies improve performance in changing market conditions.
New method avoids saddle points without gradients.
problem Optimizing non-convex functions efficiently.
method Zero-order derivative-free algorithm using only function evaluations.
result Converges to second-order stationary points efficiently.