Normal Inverse Gaussian

Quantum computing for multidimensional option pricing: End-to-end pipeline ArXiv ID: 2601.04049 “View on arXiv” Authors: Julien Hok, Álvaro Leitao Abstract This work introduces an end-to-end framework for multi-asset option pricing that combines market-consistent risk-neutral density recovery with quantum-accelerated numerical integration. We first calibrate arbitrage-free marginal distributions from European option quotes using the Normal Inverse Gaussian (NIG) model, leveraging its analytical tractability and ability to capture skewness and fat tails. Marginals are coupled via a Gaussian copula to construct joint distributions. To address the computational bottleneck of the high-dimensional integration required to solve the option pricing formula, we employ Quantum Accelerated Monte Carlo (QAMC) techniques based on Quantum Amplitude Estimation (QAE), achieving quadratic convergence improvements over classical Monte Carlo (CMC) methods. Theoretical results establish accuracy bounds and query complexity for both marginal density estimation (via cosine-series expansions) and multidimensional pricing. Empirical tests on liquid equity entities (Credit Agricole, AXA, Michelin) confirm high calibration accuracy and demonstrate that QAMC requires 10-100 times fewer queries than classical methods for comparable precision. This study provides a practical route to integrate arbitrage-aware modelling with quantum computing, highlighting implications for scalability and future extensions to complex derivatives. ...

Beyond the Traditional VIX: A Novel Approach to Identifying Uncertainty Shocks in Financial Markets ArXiv ID: 2411.02804 “View on arXiv” Authors: Unknown Abstract We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures market expectations of future volatility, but traditional methods based on second-moment shocks and time-varying volatility of the VIX often fail to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we construct a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Levy process to S&P 500 option prices, providing a more comprehensive measure of volatility that reflects the extreme movements and heavy tails observed in financial data. Using an axiomatic approach, we introduce a general family of risk-reward ratios, computed with our revised VIX and fitted over a fractional time series to more accurately identify uncertainty shocks in financial markets. ...