Implied Volatility in Decentralized Finance Pool

Abstract

We propose a "break-even" implied volatility of a decentralized finance (defi) pool. The implied volatility is "break-even" because it is defined by the zero expected profit-and-loss of hedged liquidity providers i.e. by their expected profit (against the "buy-and-hold" benchmark) equaling their expected loss (against the same benchmark): the numerator of Rebalancing Loss a.k.a. Impermanent Loss. It depends only on the time-to-maturity and therefore forms only a curve (as opposed to the traditional surface). Similarly to traditional finance, when implied volatility is higher than realized volatility, option sellers (liquidity providers) are more likely to make money, irrespective of hedging. When approximated, this first-principles definition of implied volatility can be surprisingly (loosely) derived from the square-root market impact empirical rule in traditional finance.