Computation of the implied discount rate and volatility for an overdefined system using stochastic optimization
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© 2015 The Authors. 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.
This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Management Mathematics following peer review. The version of record is available online at http://doi.org/10.1093/imaman/dpv007
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