Term Structure

Small Volatility Approximation and Multi-Factor HJM Models ArXiv ID: 2506.12584 “View on arXiv” Authors: V. M. Belyaev Abstract Here we demonstrate how we can use Small Volatility Approximation in calibration of Multi-Factor HJM model with deterministic correlations, factor volatilities and mean reversals. It is noticed that quality of this calibration is very good and it does not depend on number of factors. Keywords: Heath-Jarrow-Morton (HJM) Model, Small Volatility Approximation, Calibration, Deterministic Volatility, Term Structure, Fixed Income ...

Understanding the Commodity Futures Term Structure Through Signatures ArXiv ID: 2503.00603 “View on arXiv” Authors: Unknown Abstract Signature methods have been widely and effectively used as a tool for feature extraction in statistical learning methods, notably in mathematical finance. They lack, however, interpretability: in the general case, it is unclear why signatures actually work. The present article aims to address this issue directly, by introducing and developing the concept of signature perturbations. In particular, we construct a regular perturbation of the signature of the term structure of log prices for various commodities, in terms of the convenience yield. Our perturbation expansion and rigorous convergence estimates help explain the success of signature-based classification of commodities markets according to their term structure, with the volatility of the convenience yield as the major discriminant. ...

Markov-Functional Models with Local Drift ArXiv ID: 2411.15053 “View on arXiv” Authors: Unknown Abstract We introduce a Markov-functional approach to construct local volatility models that are calibrated to a discrete set of marginal distributions. The method is inspired by and extends the volatility interpolation of Bass (1983) and Conze and Henry-Labordère (2022). The method is illustrated with efficient numerical algorithms in the cases where the constructed local volatility functions are: (1) time-homogeneous between or (2) continuous across, the successive maturities. The step-wise time-homogeneous construction produces a parsimonious representation of the local volatility term structure. ...

A GCN-LSTM Approach for ES-mini and VX Futures Forecasting ArXiv ID: 2408.05659 “View on arXiv” Authors: Unknown Abstract We propose a novel data-driven network framework for forecasting problems related to E-mini S&P 500 and CBOE Volatility Index futures, in which products with different expirations act as distinct nodes. We provide visual demonstrations of the correlation structures of these products in terms of their returns, realized volatility, and trading volume. The resulting networks offer insights into the contemporaneous movements across the different products, illustrating how inherently connected the movements of the future products belonging to these two classes are. These networks are further utilized by a multi-channel Graph Convolutional Network to enhance the predictive power of a Long Short-Term Memory network, allowing for the propagation of forecasts of highly correlated quantities, combining the temporal with the spatial aspect of the term structure. ...