Computation of the implied discount rate and volatility for an overdefined system using stochastic optimization

Abstract

This paper studies estimation of the implied volatility and the impact of the choice of the corresponding risk-free rate proxy. We suggest to analyse the implied volatility and the risk-free rate proxy inferred in conjunction with the observed option prices. We formulate and solve an overdefined system of non-linear 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 reveal a higher inferred risk-free rate than commonly used proxies. This leads to narrower volatility spread, or smaller difference between implied and realized volatilities.