The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all parameters at once. We demonstrate that how the HMC reproduces the GARCH paramete…
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
This paper extends AD techniques to Monte Carlo processes for efficient derivative calculation.
problem Obtaining derivatives of expectation values in Monte Carlo processes.
method Two approaches: reweighting and Hamiltonian extension of HMC.
result Hamiltonian approach as a change of variables simplifies variance reduction.
We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility variables of the SV model in the Bayesian inference. We compute parameters of the SV mod…
The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integr…
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.
Efficient hybrid method for pricing barrier options with stochastic volatility.
problem Valuation of barrier options on assets with stochastic volatility.
method Combining Monte Carlo simulation and semi-analytical heat potential method.
result Our method provides better accuracy and is orders of magnitude faster than existing methods.
Study computes option sensitivities using Malliavin calculus for hybrid stochastic models.
problem Computing option sensitivities (Greeks) under hybrid stochastic volatility and interest rate models.
method Integrates Malliavin calculus for Delta, Vega, and Rho computation; extends to non-differentiable payoffs.
result Malliavin calculus enables effective numerical implementations for various option types.
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. …
The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we compute parameters of the SV model by using the artificial financial data and compare …
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.
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…
In this paper we use a hybrid Monte Carlo-Optimal quantization method to approximate the conditional survival probabilities of a firm, given a structural model for its credit defaul, under partial information. We consider the case when the firm's value is a non-observable stochastic process (Vt)t≥0 and inver…
Develops efficient Monte Carlo methods for rough volatility models.
problem Challenges in simulating rough volatility processes.
method Extension of Donsker's approximation to fractional Brownian motion.
result Justifies the validity of simple Monte Carlo methods for rough volatility models.
GPU accelerates Bayesian inference of RSV model up to 17x faster.
problem Bayesian inference of realized stochastic volatility model.
method Hybrid Monte Carlo (HMC) algorithm parallelized on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz).
result GPU can achieve up to 17 times faster computation compared to CPU.
This paper improves GP models by making them sparse and variational.
problem Efficient computation and approximation of GP models with large datasets and non-Gaussian likelihoods.
method Variational approximation to the posterior, sparse in support of the function, with efficient computations based on inducing-point sparse GPs.
result A Hybrid Monte-Carlo sampling scheme for non-Gaussian approximations of function values and covariance parameters.
We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant points in the target distribution. We prove that it is possible to introduce search…
A hybrid framework prices options using neural networks and VAE latent space.
problem Lack of explicit asset dynamics information in compressed volatility surfaces.
method Combining Weighted Monte Carlo with neural networks trained on VAE latent space.
result Effective pricing of vanilla and exotic options on idealized vol surface.
Paper derives analytical formulas for NLD-CEV moments with regime switching.
problem Analytical tractability of NLD-CEV models under stochastic regimes.
method Hybrid system approach using Feynman-Kac formula for solving interconnected PDEs.
result Exact closed-form expressions for fractional-order conditional moments.
We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …
Bayesian inference on matrix manifolds simplifies linear dimensionality reduction.
problem Linear dimensionality reduction in high dimensions.
method Bayesian inference on Grassmann and Stiefel manifolds using Hybrid Monte Carlo.
result Hybrid Monte Carlo on Grassmannian for posterior sampling.
Proposes EDESH-SA for better inventory management under uncertainty.
problem Inventory management under uncertainty.
method Ensemble Differential Evolution with simulation-based hybridization and self-adaptation.
result Improves financial performance and optimizes search spaces.
A hybrid scheme improves accuracy in simulating Brownian semistationary processes.
problem Simulating Brownian semistationary processes with high accuracy.
method Discretizing the stochastic integral representation using a hybrid scheme of power and step functions.
result The hybrid scheme leads to a substantial improvement in accuracy compared to the forward Riemann-sum scheme.
This paper modifies the Ait-Sahalia model to better describe interest rate behaviors.
problem Inadequate specifications of the original Ait-Sahalia model to explain various interest rate phenomena.
method Proposes a modified hybrid Poisson-jump Ait-Sahalia model and uses truncated EM techniques for numerical approximation.
result Validates the modified model using Monte Carlo simulations for bond and barrier option payoffs.
Hybrid model for multimodal distributions using diffusion and classification.
problem Sampling from multimodal distributions with correct proportions.
method Divide-and-conquer strategy: identify modes, train classifiers, diffusion models, bridge sampling.
result Framework effectively handles multimodal distributions in high dimensions.
A new method uses ABC-SMC to infer hybrid models in bioprocesses with limited data.
problem Inference of hybrid models in bioprocesses with limited real data and high uncertainties.
method Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) and linear Gaussian dynamic Bayesian network (LG-DBN) for posterior distribution approximation.
result The method accelerates hybrid model inference and supports process monitoring and robust control.
AutoML uses MCTS to optimize machine learning algorithms and hyperparameters.
problem Optimizing machine learning algorithms and hyperparameters efficiently.
method MCTS-based approach for hybrid optimization of machine learning portfolios.
result Mosaic outperforms Auto-Sklearn on OpenML 100 benchmark and Scikit-learn portfolio.
Framework for sensitivity analysis in biomanufacturing processes.
problem High complexity and uncertainty in biomanufacturing processes.
method Shapley value estimation for linear and nonlinear pKG models, using quasi-Monte Carlo and antithetic sampling.
result Improved efficiency and accuracy in sensitivity analysis for biomanufacturing processes.
Quantum computing speeds up interest rate derivative pricing using LMM.
problem Challenges in pricing interest rate derivatives, especially caps.
method Hybrid classical-quantum approach using quantum amplitude estimation.
result Quantum computing improves convergence in pricing interest rate derivatives.
The paper compares different models for GLWB pricing and hedging.
problem Valuing GLWB products in various models and interest rate scenarios.
method Hybrid tree-finite difference, Monte Carlo, and finite difference schemes.
result Numerical methods determine no-arbitrage fees and Greeks for GLWB contracts.
Optimized GPRNN reduces model complexity and overfitting, improving performance.
problem Overfitting in neural networks and high model complexity.
method Gaussian Process Regression - Neural Network hybrid with optimized redundant coordinates.
result Optimized GPRNN achieves lower test set error with fewer terms/neurons.
Paper estimates CVA under Bates model using efficient method for solving PIDEs.
problem Estimating Credit Value Adjustment (CVA) under Bates model with stochastic volatility and jumps.
method Proposes an efficient method replacing Monte Carlo with finite difference for solving coupled PIDEs.
result Demonstrates effectiveness and reliability of the proposed approach for European and American options.
This paper reviews various sampling methods from statistics and machine learning.
problem Addressing sampling methods in statistics and machine learning.
method Explains and reviews simple random sampling, bootstrapping, stratified sampling, cluster sampling, multistage sampling, network sampling, snowball sampling, and sampling from cumulative distribution function.
result Summarizes characteristics, pros, and cons of different sampling methods.
New MCMC methods improve sampling efficiency and mixing.
problem Improving sampling efficiency and mixing in MCMC methods.
method Sequential proposals in MCMC methods, including HMC and bouncy particle sampler.
result New methods improve numerical efficiency and mixing in multimodal distributions.
Bayesian Neural Networks improve credit card default prediction and provide feature importance.
problem Lack of interpretability and uncertainty measures in neural network models for credit risk.
method Developed and compared BNNs trained by Gaussian approximation and Hybrid Monte Carlo.
result BNNs with Automatic Relevance Determination outperform normal BNNs in credit card default prediction.
Paper extends SVI to non-conjugate models with two levels of hidden variables.
problem Non-conjugate Bayesian models with two levels of hidden variables.
method Monte Carlo Structured SVI (MC-SSVI) with improved structured variational approximation and hybrid algorithm using both standard and natural gradients.
result MC-SSVI significantly extends the scope of SVI to non-conjugate models.
The study proposes methods to price and hedge GMWB using stochastic models.
problem Valuing and hedging GMWB in the presence of stochastic interest rates and volatility.
method Hybrid tree-finite difference, Hybrid Monte Carlo, ADI finite difference, Standard Monte Carlo methods.
result Demonstrates sensitivity of no-arbitrage fee to various assumptions.
DR-MCTS improves decision quality and sample efficiency in complex environments.
problem Improving decision quality and sample efficiency in complex environments.
method Integrates Doubly Robust off-policy estimation into Monte Carlo Tree Search (MCTS).
result DR-MCTS achieves superior performance in Tic-Tac-Toe and VirtualHome tasks.
New algorithm calibrates stochastic volatility models without errors.
problem Calibration errors in stochastic volatility models.
method Monte Carlo based LSV calibration algorithm for all models.
result Closed-form and exact calibration method with variance reduction.
Quantum methods improve option pricing accuracy.
problem Pricing financial derivatives using Monte Carlo integration.
method Hybrid classical-quantum methods using Fourier series and QML.
result Quantum methods achieve remarkable accuracy in option pricing.
Improves MCMC and VI methods by optimising simulation bias.
problem Limitations of MCMC and VI methods in practice.
method Hybrid method combining optimisation with MCMC simulation.
result Produces low-biased samples with better balance between bias and efficiency.
We simplify a complex volatility model to make it easier to price options.
problem The rough Bergomi model's non-Markovian nature complicates option pricing.
method We approximate the rBergomi model with a Bergomi model that is Markovian.
result The rBergomi model can be effectively approximated by a Markovian model.
Hybrid ResNet and RMT improve covariance matrix estimation for cryptocurrency portfolios.
problem Noisy, non-Gaussian financial data leads to unstable covariance matrices.
method Combines RMT regularization and ResNet learning for data-driven corrections.
result Hybrid estimator outperforms traditional methods in portfolio optimization.
Review of MLMC in financial engineering, focusing on option pricing and risk management.
problem Efficient estimation of financial risks and option prices using Monte Carlo methods.
method Incorporation of importance sampling and adaptive sampling algorithms in MLMC framework.
result Hybrid algorithms reduce overall variance in estimating financial risks and option prices.
MPHL algorithm improves wireless network localization using distance and direction data.
problem Accurate and affordable positioning in wireless networks.
method Hybrid approach combining distance and direction estimates, statistical model, belief propagation, and MCMC sampling.
result Significant reduction in localization error, up to 50% compared to competing algorithms.
EnKO combines VI and EnKF for efficient latent dynamics inference.
problem Particle degeneracy and biased gradient estimators in SMC-based methods.
method EnKO: hybrid of VI and EnKF.
result EnKO outperforms SMC-based methods in predictive ability and particle efficiency.
A new explicit scheme calculates XVA adjustments using neural networks and conditional expectations.
problem Calculating cross valuation adjustments (XVA) in realistic financial scenarios.
method Simulation/regression scheme for BSDEs, using neural networks and quantile regressions.
result The scheme outperforms Picard iterations in high-dimensional and hybrid market risks.
Hybrid approach combines VI and HMC for efficient Bayesian inference in neural networks.
problem Computational demands and inaccuracies in Bayesian inference for neural networks.
method Combines VI and HMC, reducing parameter space and accelerating inference.
result Significantly reduces inference time for large neural networks, improving uncertainty quantification.