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.
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…
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.
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.
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.
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 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.
Paper solves convertible bond valuation using finite elements with penalty method.
problem Valuation of convertible bonds under penalty TF model.
method Solves TF system of equations using P1 and P2 finite elements with penalty method.
result Numerical solutions compare favorably with finite difference method.
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…
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.
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…
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.
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.
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.
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.
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.
Paper introduces a new reinforcement learning method with improved performance.
problem Designing and analyzing efficient reinforcement learning algorithms.
method Proximal gradient temporal difference learning (GTD) with accelerated algorithm GTD2-MP.
result GTD algorithms have linear complexity and improved convergence rate.
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…
Generalizes neural networks for infinite-dimensional mappings, including PDE solutions.
problem Learning mappings between infinite-dimensional spaces and finite-dimensional approximations.
method Graph kernel network architecture with message passing for kernel integration.
result Competitive performance compared to state-of-the-art solvers for PDEs.
Recently the so-called Atiyah conjecture about l^2-Betti numbers has been disproved. The counterexamples were found using a specific method of computing the spectral measure of a matrix over a complex group ring. We show that in many situations the same method allows to compute homology gradients, i.e. generalizations …
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…
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.
We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presen…
The paper solves a complex option pricing model using finite elements.
problem Risk-Adjusted Pricing Methodology (RAPM) Black-Scholes model with transaction costs.
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.
Policy gradient methods achieve linear convergence in simple MDPs.
problem Analyzing convergence rates of policy gradient methods in finite MDPs.
method Connections with policy iteration to show linear convergence with large step-sizes.
result Policy gradient methods succeed with large step-sizes and achieve linear rate of convergence.
Study on natural actor-critic for POMDPs with finite memory.
problem Learning in partially observed Markov decision processes with noisy observations.
method Finite actor-critic method with multi-step temporal difference learning.
result First non-asymptotic global convergence for POMDPs with function approximation.
The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.
problem Uncertainty in identifying density differences when supports overlap and densities have substantial pointwise differences.
method Analysis using the Poisson process and neural spike train decoding.
result The one-dimensional Wasserstein distance highlights meaningful density differences related to both rate and support.
Unified method for MMD variance estimation improves accuracy and computational efficiency.
problem Variance estimation for MMD in nonparametric testing.
method Unified finite-sample characterization of MMD variance through U-statistic and Hoeffding decomposition; exact acceleration method for univariate case.
result Unified estimators improve accuracy and computational efficiency for MMD variance.
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.
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.
In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method. The connections between FS-RBSDEs and optimal stopping time problems are investig…
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.
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.
An Empirical Analysis of the Advantages of Finite- v.s. Infinite-Width Bayesian Neural Networksstat.ML
Empirical study compares finite- and infinite-width BNNs, revealing performance differences under model mismatch.
problem Comparing BNNs with different widths due to conflicting model properties and inference intractability.
method Empirical comparison of finite- and infinite-width BNNs, analyzing performance under model mismatch.
result Increasing width can hurt BNN performance when the model is mis-specified, and finite-width BNNs generalize better under model mismatch.
A new option pricing model handles non-constant risk aversion and transaction costs.
problem Deriving a pricing model for options with varying risk aversion.
method Developed a transformation method to solve the penalized nonlinear PDE and used finite difference discretization.
result Derived bounds on option prices and proposed a numerical scheme.
FD-Net with Auxiliary Time Steps: Fast Prediction of PDEs using Hessian-Free Trust-Region Methodscs.LG
Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate fu…
Paper revisits Black-Scholes model, proving solution existence and measuring market uncertainty.
problem Proving existence of solution in inverse Black-Scholes model.
method Rigorous proof and empirical study using finite element method.
result New measure of market uncertainty developed.
Study numerical methods for singular FBSDEs with degenerate forward component.
problem Numerical approximation of singular fully coupled FBSDEs with degenerate forward component and non-smooth terminal condition.
method Splitting approach to treat diffusion and transport parts separately.
result The splitting method converges with rate 1/2 under structural condition.
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.
Proposes a new model for traffic flow on directed graphs.
problem Modeling advection on directed graphs for traffic flow.
method Reformulates graph advection operator as finite difference scheme; proposes DGAMGP model.
result Effective modeling of traffic flow and uncertainty as an advective process.
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.