PDE model predicts Bitcoin price using transaction network and sentiment data.
problem Predicting Bitcoin price with high accuracy.
method Partial differential equation model on Bitcoin transaction network, incorporating Google Trends Index.
result Average daily bitcoin price prediction accuracy of 0.82 over 362 days in 2017.
We analyze small price impacts in a multidimensional utility maximization problem using PDEs.
problem Small nonlinear price impacts in a multidimensional utility maximization problem.
method Asymptotic expansion using nonlinear PDEs related to ergodic control and linear parabolic PDEs.
result Leading order correction to the value function is characterized by a nonlinear second order PDE.
This research analyzes deep PDE solvers for option pricing accuracy.
problem Understanding the accuracy of deep learning methods for solving PDEs in option pricing.
method Comparative experiments with two neural network algorithms in Black--Scholes and Heston models.
result Empirical convergence rates and training times of TDGF method determined.
Hybrid LSMC-PDE method for Bermudan options under GDMR model.
problem Pricing Bermudan options under the GDMR model.
method Adapted Hybrid LSMC-PDE framework, combining Monte Carlo and PDE methods.
result Hybrid approach yields more accurate and lower error estimates than plain LSMC.
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.
In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th…
Derives PDEs for pricing RFR derivatives under a new FMM model.
problem Valuation of interest rate derivatives under a new FMM model.
method Develops PDEs and finite differences methods for numerical solution.
result First use of PDE methods for RFR derivatives valuation.
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.
New PDEs model implied volatility without prior knowledge.
problem Modeling implied volatility without prior knowledge.
method Derived backward and forward nonlinear PDEs, discussed initial and boundary conditions, solved numerically.
result Solved PDEs for implied volatility of positive stock price contingent claims.
Deep learning solves PDEs with boundary conditions for barrier options.
problem Solving PDEs with boundary conditions for barrier options.
method Employing deep learning to approximate solutions of the PDE with boundary conditions.
result Deep learning can solve PDEs with boundary conditions for barrier options.
Study evaluates Deep PDE solvers for high-dimensional option pricing, identifying key sources of error.
problem Empirical study on error analysis of Deep PDE solvers for high-dimensional option pricing.
method Comparative experiments with Deep BSDE method and other solvers, identifying three main sources of error.
result Deep BSDE method is superior and robust to option specifications, improving with larger batch sizes and fewer time steps.
The paper presents a PDE method for xVA incorporation in financial derivatives.
problem Incorporating value adjustments (xVA) in financial derivative pricing.
method Analytical solution of PDEs in the Black-Scholes framework.
result New semi-closed formulas for xVA are derived and compared to Monte-Carlo and numerical methods.
Develops a hybrid method combining LSMC and PDE for Bermudan option pricing.
problem Pricing Bermudan options on assets with stochastic volatility.
method Mixed least squares Monte Carlo and PDE method for arbitrary assets and volatility processes.
result The hybrid method outperforms standard LSMC in estimating prices and exercise boundaries.
Deep neural network approximates multivariate option pricing.
problem High-dimensional partial differential equations in option pricing.
method Deep parametric PDE method using neural networks.
result Option prices computed in milliseconds for up to 25 dimensions.
In this article we present new results for the pricing of arithmetic Asian options within a Black-Scholes context. To derive these results we make extensive use of the local scale invariance that exists in the theory of contingent claim pricing. This allows us to derive, in a natural way, a simple PDE for the price of …
Quantum algorithm for multi-asset option pricing under different volatility models.
problem Efficiently pricing multi-asset options under various volatility models using quantum computing.
method Developed an end-to-end quantum PDE framework for European option pricing, solving PDEs after discretization on spatial grids.
result Quantum framework provides polynomial improvement in resource usage compared to classical methods.
New algorithm uses deep learning for option pricing in rough volatility models.
problem Evaluating options in affine rough stochastic volatility models.
method Developed a numerical scheme based on deep learning for curve-dependent PDEs.
result Numerical simulations show the new method is a promising alternative to Monte Carlo simulations.
Paper calibrates GARCH diffusion model for option pricing using PDE methods.
problem Lack of fast, semi-analytic solution for GARCH diffusion model option pricing.
method PDE-based finite difference solver for accurate calibrations.
result PDE calibration of GARCH diffusion model to SPX options.
New quantum algorithm simplifies complex financial derivatives pricing.
problem Complex financial derivatives pricing with high dimensionality.
method Quantum-inspired variational algorithms combined with neural-network quantum states.
result Simplified pricing of European options with many correlated assets.
Study Asian option pricing under uncertain volatility, approximating prices with small volatility intervals.
problem Asian option pricing in uncertain volatility conditions.
method Procedure to approximate Asian option prices with small volatility intervals, solving fully nonlinear PDE.
result Approximation method for solving fully nonlinear PDE.
Path-dependent PDEs model VIX and Realised Variance options.
problem Modeling volatility derivatives with path-dependence.
method Continuous stochastic volatility model with Gaussian Volterra process, proving well-posedness of PDEs.
result Formulae for greeks and implied volatility provided, finite-dimensional pricing PDEs obtained in Markovian models.
Derives new equations for volatility models and option pricing.
problem Modeling and pricing options in local-stochastic-volatility models.
method Develops conditional forward equations and Dupire stochastic PDEs.
result Derives new SPDE for vanilla options.
Develops deep learning methods for non-linear PDEs in credit risk.
problem Solving option XVA pricing problems with non-linear PDE models.
method Boundary-safe PINNs approach, using automatic differentiation.
result Eliminates heuristic boundary condition weights, improves accuracy.
This article provides a new representation for pricing adjustments in derivatives.
problem Derivative pricing adjustments and XVA (Expected Value of All Risk) models.
method An Ito SDE/parabolic PDE framework to encapsulate pricing adjustments.
result A new representation that encompasses various past adjustments.
The paper develops methods to price derivatives in a time-varying, age-dependent market.
problem Pricing derivatives in a market with time-inhomogeneous volatility and age-dependent processes.
method Geometric Brownian motion model with time-varying volatility and age-dependent semi-Markov processes. Solves a non-local PDE and integral equation.
result Explicit expressions for derivative prices and hedging strategies are derived.
We adapt a model for bilateral counterparty risk to include transaction costs.
problem Modeling bilateral counterparty risk with transaction costs.
method Derived a nonlinear PDE, proved existence of solution, developed numerical scheme.
result Existence of solution to the PDE with transaction costs.
Estimates domain truncation error for option pricing PDEs.
problem Estimating error in option pricing models with domain truncation.
method Derives an estimate of domain truncation error for a multidimensional PDE system.
result Proposes a sharper error estimate for option pricing models.
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.
When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a…
The paper analyzes sensitivities of cash flows using PDEs and Hansen-Scheinkman decomposition.
problem Large-time sensitivities of cash flows in quantitative finance.
method PDE representation of pricing operator with Hansen-Scheinkman decomposition.
result Detailed convergence rates of sensitivities are provided.
New model explains CDS price discrepancies in foreign and domestic economies.
problem Explaining discrepancies in Quanto CDS prices.
method Proposes a model with four stochastic factors and jumps-at-default, derives 4D PDEs, solves numerically.
result Qualitative explanation of CDS price discrepancies.
Efficient PDE method calibrates local volatility with stochastic interest rates.
problem Calibrating local volatility models with stochastic interest rates is time-consuming.
method Developed a PDE approach using ADI method to solve the forward equation.
result Effective and sufficient information for calibration and pricing is provided.
Tensor Neural Networks solve high-dimensional PDEs for financial pricing.
problem High-dimensional PDEs in financial pricing.
method Tensor Neural Networks (TNN) and Tensor Network Initializer (TNN Init).
result TNN provides significant parameter savings and faster training than DNN.
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a…
Neural networks improve financial derivative pricing accuracy.
problem Improving accuracy in financial derivative pricing.
method Use neural networks to model drift and volatility in SDE models, optimize using SGD for European options and PDE for American options.
result Neural network models outperform traditional models in pricing derivatives.
The paper explains FX option pricing in target zones with non-deterministic short rates.
problem FX option pricing in target zones with non-deterministic short rates.
method Analytical solution of the pricing PDE with series of elementary functions.
result European option prices can be expressed via fast converging series of elementary functions.
Deep learning solves complex financial PDEs without mesh.
problem Solving high-dimensional PDEs in finance.
method Deep Galerkin Method using neural networks.
result DGM outperforms traditional methods in high dimensions.
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.
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing PDE. This can be done in a very e…
We consider assets for which price Xt and squared volatility Yt are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from N sub-sampled data (XnT,YnT), estimation errors do impact the classical option pricing PDEs. We estimate thes…
Deep learning for unbiased PDE solutions in finance.
problem Approximating unbiased derivatives and hedging strategies for high-dimensional PDEs.
method Developed deep learning algorithms approximating PDE solutions and their gradients, using Monte Carlo simulation and Martingale Representation Theorem.
result The approach removes bias in deep network approximations of PDE solutions, making it robust and suitable for high-dimensional problems.
Meta-learning base distributions for efficient PDE solutions.
problem Efficiently solving parametric parabolic PDEs across different scenarios.
method Meta-learning base distributions to compute PDE solutions.
result Improves generalization to new parameter regimes.
Study optimal liquidation under price impact ambiguity.
problem Optimal liquidation under uncertainty about price impact parameters.
method Characterization of value function and optimal strategy via semi-linear PDE.
result Increased liquidation rates due to ambiguity aversion.
New method uses tensor networks to price multi-asset options efficiently.
problem Pricing multi-asset options via classical full-grid solvers is computationally infeasible due to the curse of dimensionality.
method Quantized tensor trains (QTT) transform the d-asset Black-Scholes PDE into a tractable high-dimensional problem.
result Full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions can be computed with high accuracy.
We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ([24]). We consider a financial market consisting of a riskless asset and a risky stock with price process modelled by a geometric generalized G-Brownian motion, which features the…
Study indifference pricing for insurance policies in a regime-switching market model.
problem Indifference pricing of pure endowment policies in a stochastic-factor model with different economic regimes.
method Stochastic control approach based on Hamilton-Jacobi-Bellman equation, Feynman-Kac formula, and sensitivity analysis.
result Characterization of indifference price as a solution to a linear PDE and a backward PDE.
Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.
problem Long-term decomposition of robust pricing kernels under G-expectation.
method Proposes and analyzes three types of quadratic G-BSDEs to decompose pricing kernels.
result Pricing kernels decomposed into four components: discounting, transitory, symmetric martingale, and volatility uncertainty.
High-order compact schemes improve option pricing accuracy for stochastic volatility models.
problem Improving option pricing accuracy for stochastic volatility models with non-uniform grids.
method Fourth-order accurate compact schemes applied to option pricing PDEs for stochastic volatility models on non-uniform grids.
result Fourth-order accuracy achieved for non-zero correlation, outperforming standard schemes.