Multifactor cat bond pricing using distortion operator models with recurrent neural networks

Abstract

This paper develops a unified framework for catastrophe (CAT) bond pricing that integrates distortion operator theory with recurrent neural network (RNN) estimation. A novel peer-adjusted distortion factor is introduced, constructed from both the Wang transform and the jump-diffusion (JD) distortion operator, and calibrated using the market-weighted spread of comparable CAT bonds together with the target bond’s expected loss. This factor embeds prevailing investor sentiment, reinsurance capacity, and market liquidity into the distortion measure, enabling consistent pricing inference even when the bond’s own spread is unobserved. Empirically, the JD distortion model systematically outperforms both the canonical Wang transform and the raw expected loss in in-sample and out-of-sample tests, capturing discontinuous repricing and tail-risk compensation with greater precision. Extending the framework to a multifactor specification that combines actuarial fundamentals with financial-market covariates further enhances explanatory and predictive performance. From a methodological perspective, the RNN serves as a structural estimator for the parameters of the distortion operators, achieving higher accuracy, stability, and computational efficiency than conventional approaches such as MLE, GMM, or ensemble regressors. By unifying distortion operators with neural estimation, this study advances both the methodological and empirical foundations of CAT bond pricing within actuarial science.