A Probabilistic Spatial Interaction Model for Bond Trading Forecasting

Abstract

This paper proposes a constrained spatial transition model for forecasting bond-trading activity at the transaction level. Instead of modeling only aggregate yield-curve characteristics, the method represents daily trades as binary states on a two-dimensional tenor–G-spread grid. For each cell, the probability of activity on the next trading date depends on the current state of the same cell and on the numbers of active cells in the first and second neighborhood rings. Linear and quadratic neighborhood terms are included to capture local interaction effects. Explicit parameter constraints keep all transition probabilities strictly between zero and one, which provides a valid finite-state Markov model and supports results on existence, irreducibility, aperiodicity, ergodicity, identifiability, and consistency of the constrained least-squares estimator.

The empirical study uses 17,943 bond observations for six medical-sector issuers over 345 trading dates. The data are divided chronologically into training, validation, and held-out test periods. Grid resolution and neighborhood size are selected using validation data only. Statistical significance is assessed using moving-block bootstrap confidence intervals, circular-shift permutation tests, and Benjamini–Hochberg correction. On the held-out test sample, the proposed model achieves an F1 score of 0.697, ROC–AUC of 0.842, PR–AUC of 0.640, Brier score of 0.101, and log loss of 0.321. It outperforms persistence, a first-order Markov baseline, and logistic regression, while random forest and gradient boosting provide slightly higher predictive accuracy. Predicted active cells are also used to reconstruct continuous G-spread curves with modified Nelson–Siegel and Svensson forms. The modified Nelson–Siegel reconstruction achieves RMSE 0.694, MAE 0.551, and R² = 0.9967 on held-out dates.

JEL Classification: 91B26, 60G35, 91G30, 91B70, 60J20, 62M20.