A mathematical formulation of the valuation of gold as an inflation hedge in the United States

The literature has long viewed gold as an inflation hedge. The reasoning is that when inflation rises due to macroeconomic fluctuations, volatility in the financial markets fails to satisfy investor fears of instability in asset prices. Investors are attracted to gold due to its ability to hold its value during periods of market turbulence. The purpose of this paper is to value gold mathematically in terms of its ability to serve as an inflation hedge, and its value from an investor’s risk-taking propensity. The paper assesses the perceptions of three types of investors about gold prices. Risk-averse investors are modeled as adopting the Arrow-Pratt coefficient of risk-aversion. Moderate risk-takers’ expectations of gold prices are modeled as using Laplace transform to modify gold price expectations as additional information is received. Risk-takers’ gold price expectations are modeled as an exponential distribution. As gold prices spike during periods of uncertainty, such as the financial crisis of 2007-2008 and the ten-month high interest rate-period of 2023-2024, this paper models gold prices as a Levy jump process, with jumps representing periods of surges in gold prices. Empirical validation of gold price changes over time are included to support the theoretical formulations. The paper makes the contributions of 1) providing a mathematical basis for the movement of gold prices over time, 2) including investor risk-taking as a determinant of gold prices, and 3) empirical validation of the theoretical contribution to provide validation of theoretical propositions.