Computation of the implied discount rate and volatility for an overdefined system using stochastic optimization - Hin, L.; Dokuchaev, Nikolai (Oxford University Press, 2015)
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.