文献类型：期刊文献

英文题名：The inverse Cox-Ingersoll-Ross process for parsimonious financial price modelling

作者：Lin, L.[1];Sornette, D.[2,3]

机构：[1]East China Univ Sci & Technol, Sch Business, Shanghai 200237, Peoples R China;[2]Southern Univ Sci & Technol, Inst Risk Anal Predict & Management Risks X, Shenzhen 518055, Peoples R China;[3]Univ Geneva, Swiss Finance Inst, 40 Blvd Du Pont Arve, CH-1211 Geneva 4, Switzerland

年份：2026

外文期刊名：QUANTITATIVE FINANCE

收录：;Scopus(收录号：2-s2.0-105045642998);WOS:【SSCI(收录号:WOS:001828454700001)，SCI-EXPANDED(收录号:WOS:001828454700001)】；

基金：This work is partially supported by the National Natural Science Foundations of China [grant number 71771086 and grant number T2350710802], Shenzhen Science and Technology Innovation Commission Project [grant number K23405006], and the Center for Computational Science and Engineering at Southern University of Science and Technology.

语种：英文

外文关键词：Asset pricing; Financial risks; Financial bubbles; Excess volatility; Fat-tailed distribution of returns; Equity puzzle; Earning yield; Earning-over-price

摘要：We construct new classes of financial price processes based on the insight that the key variable driving prices P is the earning-over-price ratio gamma similar or equal to 1/P , interpreted as the earning yield and analogous to the yield-to-maturity of a perpetual bond. Modelling gamma as a Cox-Ingersoll-Ross (CIR) process, we derive analytically several stylised facts of financial markets, including power law distributed returns, transient super-exponential bubble dynamics, and fat-tailed price distributions prior to crashes. The framework explains excess volatility and the equity premium as emergent consequences of stochastic fluctuations in the discount rate, whose nonlinear inversion into prices generates an amplification factor and a positive risk premium absent in constant-rate models. The model is calibrated to five well-known historical bubbles in the US and China stock markets via a quasi-maximum likelihood method with the L-BFGS-B optimisation algorithm. Using phi-divergence statistics adapted to models prescribed in terms of stochastic differential equations, we show the superiority of the CIR process for gamma t against three alternative models.