bayesian option pricing

This study addresses the quantification of sources of predictive uncertainty and their contributions to prediction interval width. Building upon the law of total variance, the work proposes several conservative decompositions of posterior predictive variance, systematically characterizing the components of uncertainty and their interdependencies through conditional expectation and conditional variance terms. Experimental evaluations across multiple canonical models demonstrate that the proposed approach effectively identifies the dominant sources of uncertainty and reveals coherent patterns of co-variation among decomposition terms. These insights offer a novel perspective for model assessment and refinement, enhancing interpretability and guiding targeted improvements in predictive reliability.

This study addresses the limited pricing accuracy in fractional Black–Scholes models, which stems from estimation uncertainty in both the Hurst parameter and volatility. The authors propose the first Bayesian joint inference framework that models asset dynamics via fractional Brownian motion and employs Markov chain Monte Carlo (MCMC) methods to simultaneously estimate the Hurst parameter and volatility. By fully propagating posterior uncertainty into the resulting option price distribution, the approach not only overcomes the challenge of coupled parameter estimation inherent in conventional point-estimate methods but also enables rigorous quantification of pricing uncertainty. Numerical simulations and empirical analyses on WTI crude oil and natural gas options demonstrate that the method yields stable parameter estimates and reveals that observed market differences are primarily driven by variations in volatility rather than long-memory effects.

This study addresses the estimation risk inherent in parametric portfolio strategies, which traditionally rely on return-generating models and struggle to effectively integrate prior knowledge with empirical data. The authors propose a generalized Bayesian framework that updates investor beliefs about feature tilts and out-of-sample returns solely through the utility function, bypassing the need to specify a return-generating process. A key innovation is the introduction of a unique belief-updating rule aligned with investor utility, coupled with the KNEEDLE algorithm that endogenously selects the optimal scaling parameter λ* without requiring out-of-sample validation. Theoretical analysis reveals a direct link between λ* and both risk aversion and higher-order moments of returns. Empirical results using U.S. equity data from 1955 to 2024 show that feature-based predictability is largely concentrated before 2000, and that adaptive selection of λ* substantially enhances portfolio robustness.

Gaussian processes (GPs) in surrogate modeling are highly sensitive to misspecification of covariance hyperparameters—particularly the length-scale parameter θ. While fully Bayesian hierarchical inference improves robustness and uncertainty quantification, its performance critically depends on the choice of prior distributions and Markov Chain Monte Carlo (MCMC) proposal mechanisms—a dependency lacking systematic evaluation in prior work. This paper conducts the first comprehensive study of how alternative priors for θ (uniform, Gamma, inverse-Gamma) and their corresponding MCMC proposals affect posterior sampling efficiency, convergence speed, and predictive performance. Leveraging both synthetic and real-world benchmarks under Bayesian GP inference, we demonstrate that principled alignment between prior and proposal distributions significantly enhances prediction accuracy, improves uncertainty calibration, and accelerates MCMC convergence. Our empirical findings provide actionable guidelines and practical design principles for hyperparameter prior selection in Bayesian GP modeling.

This study addresses the neglect of parameter uncertainty and limited interpretability in calibrating rough volatility models by proposing a simulation-based inference framework. Methodologically, neural ratio estimation is employed to learn the posterior distribution of the rough Heston (rHeston) model, which is combined with heteroscedastic neural network surrogate pricing to generate exotic option price intervals that incorporate uncertainty. Furthermore, an information-theoretic interpretability approach termed Hellinger-SHAP is introduced to quantify prior-to-posterior information contraction, thereby identifying critical parameter regions. Experimental results demonstrate that the proposed method achieves robust coverage across various exotic options within posterior predictive intervals, significantly enhancing both the reliability and transparency of derivative pricing.

This study proposes a unified model integrating the Heston stochastic volatility, Bates jump-diffusion, and Cox-Ingersoll-Ross (CIR) stochastic interest rate frameworks to jointly address mid- to short-term equity option pricing and interest rate risk assessment. The model calibrates volatility and jump parameters using Lewis’s Fourier inversion and the Carr-Madan FFT method, while the CIR component is calibrated to Euribor data to generate economically plausible forward rate paths. Empirical results indicate that jump effects are negligible within 60 days, with stochastic volatility dominating short-term pricing dynamics, whereas stochastic interest rates exert a significant influence on valuations beyond one year. The model exhibits stable parameter estimates and produces forward rate trajectories consistent with economic intuition, thereby confirming the robustness of the standard Heston/Bates framework for mid- to short-term option pricing.

This study addresses the vulnerability of traditional Bayesian posterior inference to model misspecification, which arises when the likelihood function fails to accurately characterize the underlying data-generating mechanism. To overcome this limitation, this work reconstructs Bayesian theory from a variational perspective and proposes a generalized Bayesian inference framework. By integrating variational inference with robust statistical techniques, it establishes a novel paradigm for variational posteriors under model misspecification. This research effectively mitigates the challenges posed by misspecified models, substantially broadening the applicability of Bayesian inference. Furthermore, it enhances both the reliability and precision of uncertainty quantification and parameter estimation in non-ideal modeling conditions.

This study addresses the challenge of simultaneously achieving precise local shape control and strict static no-arbitrage compliance in implied volatility curve modeling. To this end, it proposes a parsimonious and interpretable parametric approach grounded in the risk-neutral distribution. By introducing parameters that exhibit stable cross-maturity patterns, the method directly governs local curvature characteristics—such as convexity and concavity—while inherently satisfying no-arbitrage constraints. The resulting model flexibly accommodates diverse curvature patterns and supports both term structure interpolation and dynamic modeling. Empirical validation on a two-year dataset of S&P 500 options, encompassing over 250,000 calibrated volatility curves, demonstrates the stability, generalizability, and high fidelity of the proposed parameterization in capturing complex market dynamics.

This study addresses the lack of theoretical guarantees regarding the impact of predictive design distributions on inference validity in high-dimensional Bayesian regression. The authors propose a novel parametric martingale posterior approach based on sequential one-step-ahead predictive quantities, which operates without Markov chain Monte Carlo methods and, for the first time, systematically elucidates the critical role of predictive design distributions. The method satisfies weak identifiability and design invariance, and integrates predictive resampling with high-dimensional regularization techniques. In simulation experiments, it demonstrates both computational efficiency and stable performance in Bayesian predictive inference.

This work addresses the challenge of efficient sampling and uncertainty quantification for posterior distributions under general constraints by proposing an extended weighted Bayesian bootstrap method, which is the first to generalize this approach to arbitrary constraint settings. By integrating convex optimization techniques, the method approximates the constrained posterior distribution even in scenarios where conventional approaches yield only point estimates. Theoretical analysis demonstrates that the asymptotic covariance of the generated samples aligns with that of the constrained maximum likelihood estimator, ensuring both computational efficiency and statistical validity. Empirical evaluations confirm the method’s broad applicability across diverse constrained Bayesian inference problems, including a successful application to uncertainty quantification for European option price surfaces.