Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate
17 Pages Posted: 12 May 2016
Date Written: May 9, 2016
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.
Keywords: Gauge Theory, Risk Free Rate, Option Pricing
Suggested Citation: Suggested Citation