Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate

TL;DR

This paper introduces a gauge-invariant framework for defining risk-free portfolios and rates, interpreting the risk-free rate as a measure of global price rescaling symmetry, and rederives the Black-Scholes equation within this context.

Contribution

It proposes a novel gauge-invariant approach to defining risk-free portfolios and interprets the risk-free rate as a gauge symmetry parameter, offering new insights into financial modeling.

Findings

Risk-free rate as a gauge symmetry of economies

Reinterpretation of Black-Scholes equation with gauge fields

Gauge invariant discounting of cash flows

Abstract

We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits. This definition identifies the risk-free rate as the return of an infinitely diversified portfolio rather than as an arbitrary external parameter. The risk-free rate measures the rate of global price rescaling, which is a gauge symmetry of economies. We explore the properties of risk-free rates, rederive the Black Scholes equation with a new interpretation of the risk-free rate parameter as a that background gauge field, and discuss gauge invariant discounting of cash flows.