This paper implements an algorithm that can be used to solve systems of Black-Scholes equations for implied volatility … for implied volatility and implied risk-free rate, the options are re-priced using these parameters in the Black … risk-free rate model is better for predicting future evolutions in model-free implied volatility as measured by the VIX …

Conventional financial theory considers ex-ante that risk, generally measured by the volatility, has to be …