A new financial system with ethics risk modeled using fractional calculus.
problem Modeling financial systems with ethical considerations and market confidence.
method Introduced a five-dimensional conformable derivative financial system and a discretization scheme.
result Numerical solutions of the conformable derivative system were tested for hyperchaos.
The paper optimizes financial derivatives for market completion in SV models.
problem Optimizing financial derivatives for market completion in stochastic volatility models.
method Simulation-based method to approximate optimal portfolio strategy, using double optimization approach (utility maximization and risk exposure minimization).
result Strangle options are the best choices for market completion in equity options.
Smart contracts create digital financial derivatives.
problem Creating a new digital financial derivative contract.
method Applied existing smart contract technologies to develop two prototypes.
result Demonstrated feasibility of digital financial derivatives on centralized and DLT platforms.
Paper uses IGA for efficient pricing of financial derivatives, comparing it to FDM and FEM.
problem Efficiently pricing complex financial derivatives with high accuracy.
method Isogeometric Analysis (IGA) for solving nonlinear Black-Scholes PDEs.
result IGA provides very accurate solutions with fewer knots, significantly reducing computational time.
Nonparametric pricing and hedging of exotic derivatives using signature payoffs.
problem Pricing and hedging exotic derivatives accurately and efficiently.
method Introducing signature payoffs and using them to approximate and price exotic derivatives nonparametrically.
result Signature payoffs enable accurate and computationally tractable pricing and hedging of exotic derivatives.
This paper uses Malliavin calculus to price and compute delta of financial derivatives in jump-diffusion models.
problem Pricing and delta computation of financial derivatives in jump-diffusion models with stochastic intensity.
method Utilizes Malliavin calculus to price and compute delta, applying the Euler scheme for convergence analysis.
result Established the convergence of approximated solution, financial derivative, and its delta Greeks.
Novel approach to financial derivatives pricing using rough path theory.
problem No-arbitrage conditions in financial markets necessitating precise integration methods.
method Developed a polynomial-based approximation class for rough path functionals, extending to non-geometric rough paths.
result Motivated a hypothesis for payoff functionals in financial markets, facilitating analysis.
Develops trinomial models using cubature methods for financial derivative pricing.
problem Pricing financial derivatives in complex stochastic market models.
method Cubature methods applied to Wiener space for constructing trinomial models.
result Numerical solutions compare favorably with Black-Scholes model.
Quantitative structuring is a rigorous framework for the design of financial products. We show how it incorporates traditional investment ideas while supporting a more accurate expression of clients' views. We touch upon adjacent topics regarding the safety of financial derivatives and the role of pricing models in pro…
Deep learning for financial derivatives pricing and hedging.
problem Model-free pricing and optimal hedging of financial derivatives.
method Neural networks for offline training and online application.
result Accurate model-free price bounds and optimal hedging strategies.
Quantum algorithms accelerate financial risk computation.
problem Accelerating the computation of financial market risk.
method Quantum gradient estimation algorithms for market sensitivities.
result Significant reduction in resource requirements for financial quantum advantage.
We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion and multivariate Rosenblatt motion. Conditions for no-arbitrage and market comp…
Revises derivative pricing post financial crisis by defining a discount rate.
problem Derivative pricing became complex with XVA adjustments.
method Developed a binomial tree model for pricing with counterparty and funding risks.
result Coherent XVAs naturally result from decomposing the discount rate.
Financial derivatives based on road travel times for hedging and pricing.
problem Market risk in crypto and banking sectors.
method Modeling travel time data with CARMA models and applying risk-neutral pricing.
result Derivatives pricing based on travel time and its volatility.
Improved path integral method for financial derivatives pricing.
problem Analytical intractability of financial derivative pricing models.
method Generalized semi-classical path integral approach to time-dependent Hamiltonians.
result Accuracy and computational efficiency of the path integral approach for derivatives pricing.
Quantum algorithms improve VaR and CVaR estimation for financial derivatives.
problem Quantum advantage in financial risk analysis of derivatives.
method Two quantum algorithms: QSP and QSP-based approach.
result QSP-based approach requires fewer quantum resources for the same accuracy.
In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existin…
Improved price bounds for financial derivatives using time-homogeneous stock movements.
problem Deriving robust price bounds for financial derivatives under time-homogeneous stock movements.
method Variant of martingale optimal transport problem with time-homogeneity assumption.
result Improved price bounds are derived, incorporating market data from multiple time points.
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.
New method uses DistRL to estimate entire payoff distribution for financial derivatives.
problem Traditional methods focus on expected option value; this tackles risk-aware pricing.
method Reinterprets and proposes a framework using Distributional Reinforcement Learning (DistRL).
result Demonstrates enhanced risk-aware pricing and uncertainty quantification on Asian options.
Paper uses neural nets for financial optimization problems.
problem Financial optimization and derivative pricing problems.
method Neural networks and deep reinforcement learning for solving PDEs and dynamic optimization.
result Efficient resolution of nonlinear PDEs and dynamic optimization in finance.
Framework for robust control under model uncertainty, improving financial derivatives hedging.
problem Model uncertainty in financial derivatives hedging.
method Dynamic programming principle for solving one-step optimization problems.
result Robust hedging strategy outperforms model-based strategies during adverse scenarios.
Estimates cross-impact on derivatives markets using E-Mini futures and options.
problem Empirical estimation of cross-impact on complex financial instruments like derivatives.
method Modeling derivatives prices as a function of stochastic factors and trades on both factors and derivatives.
result Simple framework successfully captures cross-impact on derivatives markets.
Derives conditions for no arbitrage in financial markets with stochastic or diffusion models.
problem Existence and absence of arbitrage in financial markets with stochastic or diffusion models.
method Integral tests, martingale and strict local martingale properties of stochastic exponentials, Markov switching models.
result Conditions for the existence of minimal martingale measure and its preservation under Markov switching.
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.
Paper improves fraud detection in imbalanced financial data.
problem Detecting fraud in imbalanced financial datasets.
method Uses time-varying Poisson processes for fraud prediction.
result Method outperforms baseline in imbalanced data.
This paper uses crypto derivatives data to estimate yield curves for cryptocurrencies.
problem Estimating yield curves for cryptocurrencies without bond markets.
method Using mathematical tools and data from cryptocurrency derivatives markets.
result Yield curves can be constructed for cryptocurrencies using derivative data.
New methods solve SPDEs for financial derivative pricing.
problem Deriving the price of financial derivatives using SPDEs.
method Developed a conditional Feynman-Kac formula to solve SPDEs.
result Established new numerical methods for mixed Monte-Carlo PDEs.
Enhanced stock market strategy using stress index and financial news sentiment analysis.
problem Improving risk assessment and prediction in equity markets.
method Combines financial stress indicator with sentiment analysis of financial news.
result Improved performance with higher Sharpe ratio and reduced drawdowns.
The paper approximates financial derivatives using neural networks and iterated integrals.
problem Approximating p-integrable financial derivatives. method Using iterated Stratonovich integrals and neural networks.
result Approximate solutions to the Lp-hedging problem. The paper calculates sensitivities for financial derivatives using path weighting methods.
problem Computing sensitivities for path-dependent financial derivatives with high variance and degeneracy issues.
method Proposes explicit path weighting formula, variance reduction adjustment, and covariance inflation technique.
result Effective methods to address high variance and degeneracy in sensitivities computation.
Deep Bellman Hedging uses reinforcement learning to optimize financial portfolio hedging.
problem Optimizing financial portfolio hedging with derivatives and trading frictions.
method Actor-critic reinforcement learning algorithm with continuous state and action spaces.
result Trained model provides optimal hedge for any initial portfolio and market state.
A neural network method improves CVA computations for complex financial portfolios.
problem Improving accuracy of CVA computations for large, diverse portfolios of financial derivatives.
method Proposes a neural network-based approach to adjust exercise strategies for counterparty default risk.
result Shows significant overestimation of CVA by standard methods, especially for non-extreme cases.
The recent financial crisis have generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the "financial contagion" process in which insolvencies of individual entities propagate through the…
Arora, Barak, Brunnermeier, and Ge showed that taking computational complexity into account, a dishonest seller could strategically place lemons in financial derivatives to make them substantially less valuable to buyers. We show that if the seller is required to construct derivatives of a certain form, then this pheno…
The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.
Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on financial assets. Using a recent model for market dynamics which adequately captures …
Mathematical framework for differential machine learning in finance.
problem Theoretical assumptions in financial models and their impact on machine learning algorithms.
method Rigorous mathematical framework for differential machine learning in finance.
result Theoretical grounding enhances the predictive capabilities of neural networks in financial applications.
This paper extends the Black-Scholes-Merton model to more complex market scenarios.
problem Extending the Black-Scholes-Merton model to more complex market scenarios.
method Develops a new approach using Martingale Optimal Transport to replicate financial derivatives under extreme market models given marginals.
result Demonstrates the existence of a portfolio that replicates the payoff of a path-dependent derivative security under various market models.
Quantum model investigates financial derivative price dynamics with quantum interference effects.
problem Investigate quantum drift in financial derivatives using Heisenberg Equation of Motion.
method Apply geometric techniques to integrate Heisenberg Equation of Motion, model financial market as quantum observable.
result Quantum interference effects can act as drag or boost on financial returns.
Study uncovers CDS anomalies leading to arbitrage profits.
problem Identifying arbitrage opportunities in CDS term structures.
method Derive No-arbitrage conditions for CDS term structures, analyze extensive dataset.
result Presented 2,416 pairs of anomalous CDS contracts.
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of f…
Monte Carlo Tree Search improves financial derivative hedging efficiency.
problem Optimizing pricing and hedging of derivative contracts in incomplete markets.
method Integrates tree search techniques with Reinforcement Learning for optimal control problems.
result Monte Carlo Tree Search outperforms Q-learning in sample efficiency and learning speed. The article reviews how to set stochastic volatility model parameters.
problem Choosing parameters for stochastic volatility models.
method Examines existing literature on various methods.
result Different approaches to setting stochastic volatility parameters.
DHLNN improves deep hedging for financial derivatives with faster convergence and better stability.
problem Challenges in computational inefficiency, sensitivity to noisy data, and optimization complexity in deep hedging methods.
method Integrates periodic fixed-gradient optimization and linearized training dynamics to stabilize and accelerate deep learning model training.
result Demonstrates faster convergence, improved stability, and superior hedging performance across diverse market scenarios.
Quantum algorithm speeds up pricing of financial derivatives.
problem Pricing autocallable options efficiently.
method Integration-based exponential amplitude loading technique.
result 50x reduction in circuit depth for payoff component.
We shall study backward stochastic differential equations and we will present a new approach for the existence of the solution. This type of equation appears very often in the valuation of financial derivatives in complete markets. Therefore, the identification of the solution as the unique element in a certain Banach …
Quantum algorithms for financial derivatives and credit risk.
problem Estimating credit risk and option pricing in realistic financial models.
method Developed a regime switching volatility model for financial markets, using a Markov chain to determine volatility parameters.
result Quantum algorithms can be applied to realistic financial models, bringing quantum computing closer to practical applications.