A Parsimonious Inverse Cox-Ingersoll-Ross Process for Financial Price Modeling

49 Pages Posted: 28 Feb 2023 Last revised: 9 Jun 2023

See all articles by Li Lin

Li Lin

East China University of Science and Technology (ECUST)

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech); Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Tokyo Institute of Technology

Date Written: February 22, 2023

Abstract

We propose a formulation to construct new classes of financial price processes based on the insight that the key variable driving prices P is the earning-over-price ratio γ ≃ 1/ P, which we refer to as the earning yield and is analogous to the yield-to-maturity of an equivalent perpetual bond. This modeling strategy is illustrated with the choice for real-time γ in the form of the Cox-Ingersoll-Ross (CIR) process, which allows us to derive analytically many stylised facts of financial prices and returns, such as the power law distribution of returns, transient super-exponential bubble behavior, and the fat-tailed distribution of prices before bubbles burst. Our model sheds new light on rationalizing the excess volatility and the equity premium puzzles. 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 optimization algorithm. Using ϕ-divergence statistics adapted to models prescribed in terms of stochastic differential equations, we show the superiority of the CIR process for γt against three alternative models.

Keywords: asset pricing, financial risks, financial bubbles, excess volatility, fat tail distribution of returns, equity puzzle, earning yield, earning-over-price

JEL Classification: G01; G12

Suggested Citation

Lin, Li and Sornette, Didier, A Parsimonious Inverse Cox-Ingersoll-Ross Process for Financial Price Modeling (February 22, 2023). Swiss Finance Institute Research Paper No. 23-41, Available at SSRN: https://ssrn.com/abstract=4366971 or http://dx.doi.org/10.2139/ssrn.4366971

Li Lin (Contact Author)

East China University of Science and Technology (ECUST) ( email )

Shanghai
China

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech) ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Swiss Finance Institute ( email )

c/o University of Geneva
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CH-1211 Geneva 4
Switzerland

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

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Zurich, ZURICH CH-8092
Switzerland
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41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Tokyo Institute of Technology ( email )

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Tokyo 152-8550, 52-8552
Japan

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