An Analysis of Volatility Spread via the Risk-Free Rate Proxy

Abstract

The paper studies estimation of implied volatility and the impact of the choice of the corresponding risk-free rate proxy. We suggest to analyze the implied volatility and the risk-free rate proxy inferred in conjunction from the observed option prices. We formulate and solve an overdefined system of nonlinear equations for the Black-Scholes model using options data. More precisely, we seek an optimal approximate solution via differential evolution, a stochastic optimization technique. Some experiments with historical prices reveals higher inferred risk-free rate than commonly used proxies. This leads to narrower volatility spread, or the difference between implied and realized volatilities.

Keywords: implied volatility, optimization, risk-free rate

JEL Classification: C14, C51, C58, C61, G13