Volatility Modelling

Efficient Calibration in the rough Bergomi model by Wasserstein distance ArXiv ID: 2512.00448 “View on arXiv” Authors: Changqing Teng, Guanglian Li Abstract Despite the empirical success in modeling volatility of the rough Bergomi (rBergomi) model, it suffers from pricing and calibration difficulties stemming from its non-Markovian structure. To address this, we propose a comprehensive computational framework that enhances both simulation and calibration. First, we develop a modified Sum-of-Exponentials (mSOE) Monte Carlo scheme which hybridizes an exact simulation of the singular kernel near the origin with a multi-factor approximation for the remainder. This method achieves high accuracy, particularly for out-of-the-money options, with an $\mathcal{“O”}(n)$ computational cost. Second, based on this efficient pricing engine, we then propose a distribution-matching calibration scheme by using Wasserstein distance as the optimization objective. This leverages a minimax formulation against Lipschitz payoffs, which effectively distributes pricing errors and improving robustness. Our numerical results confirm the mSOE scheme’s convergence and demonstrate that the calibration algorithm reliably identifies model parameters and generalizes well to path-dependent options, which offers a powerful and generic tool for practical model fitting. ...

Predicting Stock Market Crash with Bayesian Generalised Pareto Regression ArXiv ID: 2506.17549 “View on arXiv” Authors: Sourish Das Abstract This paper develops a Bayesian Generalised Pareto Regression (GPR) model to forecast extreme losses in Indian equity markets, with a focus on the Nifty 50 index. Extreme negative returns, though rare, can cause significant financial disruption, and accurate modelling of such events is essential for effective risk management. Traditional Generalised Pareto Distribution (GPD) models often ignore market conditions; in contrast, our framework links the scale parameter to covariates using a log-linear function, allowing tail risk to respond dynamically to market volatility. We examine four prior choices for Bayesian regularisation of regression coefficients: Cauchy, Lasso (Laplace), Ridge (Gaussian), and Zellner’s g-prior. Simulation results suggest that the Cauchy prior delivers the best trade-off between predictive accuracy and model simplicity, achieving the lowest RMSE, AIC, and BIC values. Empirically, we apply the model to large negative returns (exceeding 5%) in the Nifty 50 index. Volatility measures from the Nifty 50, S&P 500, and gold are used as covariates to capture both domestic and global risk drivers. Our findings show that tail risk increases significantly with higher market volatility. In particular, both S&P 500 and gold volatilities contribute meaningfully to crash prediction, highlighting global spillover and flight-to-safety effects. The proposed GPR model offers a robust and interpretable approach for tail risk forecasting in emerging markets. It improves upon traditional EVT-based models by incorporating real-time financial indicators, making it useful for practitioners, policymakers, and financial regulators concerned with systemic risk and stress testing. ...

A Dynamic Approach to Stock Price Prediction: Comparing RNN and Mixture of Experts Models Across Different Volatility Profiles ArXiv ID: 2410.07234 “View on arXiv” Authors: Unknown Abstract This study evaluates the effectiveness of a Mixture of Experts (MoE) model for stock price prediction by comparing it to a Recurrent Neural Network (RNN) and a linear regression model. The MoE framework combines an RNN for volatile stocks and a linear model for stable stocks, dynamically adjusting the weight of each model through a gating network. Results indicate that the MoE approach significantly improves predictive accuracy across different volatility profiles. The RNN effectively captures non-linear patterns for volatile companies but tends to overfit stable data, whereas the linear model performs well for predictable trends. The MoE model’s adaptability allows it to outperform each individual model, reducing errors such as Mean Squared Error (MSE) and Mean Absolute Error (MAE). Future work should focus on enhancing the gating mechanism and validating the model with real-world datasets to optimize its practical applicability. ...

Dynamically Consistent Analysis of Realized Covariations in Term Structure Models ArXiv ID: 2406.19412 “View on arXiv” Authors: Unknown Abstract In this article we show how to analyze the covariation of bond prices nonparametrically and robustly, staying consistent with a general no-arbitrage setting. This is, in particular, motivated by the problem of identifying the number of statistically relevant factors in the bond market under minimal conditions. We apply this method in an empirical study which suggests that a high number of factors is needed to describe the term structure evolution and that the term structure of volatility varies over time. ...