An Empirical Implementation of the Shadow Riskless Rate

Paper: arXiv 2411.07421

Authors: Davide Lauria, JiHo Park, Yuan Hu, W. Brent Lindquist, Svetlozar T. Rachev, Frank J. Fabozzi

Abstract

We address the problem of asset pricing in a market where there is no risky asset. Previous work developed a theoretical model for a shadow riskless rate (SRR) for such a market in terms of the drift component of the state-price deflator for that asset universe. Assuming asset prices are modeled by correlated geometric Brownian motion, in this work we develop a computational approach to estimate the SRR from empirical datasets. The approach employs: principal component analysis to model the effects of the individual Brownian motions; singular value decomposition to capture the abrupt changes in condition number of the linear system whose solution provides the SRR values; and a regularization to control the rate of change of the condition number. Among other uses (e.g., for option pricing, developing a term structure of interest rate), the SRR can be employed as an investment discriminator between asset classes. We apply the computational procedure to markets consisting of groups of stocks, varying asset type and number. The theoretical and computational analysis provides not only the drift, but also the total volatility of the state-price deflator. We investigate the time trajectory of these two descriptive components of the state-price deflator for the empirical datasets.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper bridges theoretical asset pricing and computational finance by creating an empirical framework for the Shadow Riskless Rate (SRR) using PCA, SVD, and regularization. The mathematical derivation using state-price deflators is rigorous, and the empirical application to stock and ETF market data provides practical insight into financial markets lacking traditional safe assets.

Research Flowchart

  flowchart TD
    A[Research Goal: Estimate Shadow Riskless Rate SRR<br/>in markets without a riskless asset] --> B[Data Inputs: Empirical stock market datasets<br/>modeled via Geometric Brownian Motion]
    
    B --> C[Computational Pipeline:<br/>1. PCA for Brownian motion effects<br/>2. SVD for linear system stability<br/>3. Regularization for condition number control]
    
    C --> D[Outputs & Findings:<br/>1. SRR estimation drift component<br/>2. Total volatility of state-price deflator<br/>3. Trajectory analysis for asset discrimination]

Cited References (27)

1. A Theory of Safe Asset Creation, Systematic Risk, and Aggregate Demand (2023) — link
2. Safe asset shortages and asset price bubbles (2014)
3. Exponentially decreasing distributions for the logarithm of particle size (1977)
4. Capital Market Equilibrium with Restricted Borrowing (1972)
5. Risk-sharing externalities (2023)
6. A Model of the Safe Asset Mechanism ( SAM ): Safety Traps and Economic Policy (2013) — link
7. The Safety Trap (2018)
8. A risk-centric model of demand recessions and speculation (2020)

0 of 27 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.