Econometric specification of the risk neutral valuation model (Q1969816)

For a given option price, the Black-Scholes model implies the volatility parameter \(\sigma\). For different options \(i\) the implied \(\sigma_i\) will vary depending, e.g., on the moneyness of the option (volatility smile). The authors provide an option valuation model that explains this by introducing a stochastic risk neutral measure representing information available to traders but not to the statistician. The option prices can then be considered to be stochastic as well. By selecting a suitable model for the stochastic information, and parameterizing it, it is possible to fit the (additional) parameters based on observed prices. Other models exist which try to explain the differences in volatility, some of the alternatives are mentioned in the paper.