Genetically derived approximations for determining the implied volatility

In established option valuation models all parameters except for the volatility can be observed from market data. The volatility can be calculated either from historical data (historical volatility) or implicitly by using the current option price in the valuation model (implied volatility). However, calculating the exact implied volatility manually is error-prone and spreadsheet implementations are cumbersome. Therefore analytical approximations are applied more often for determining the implied volatility. In this paper we derive analytical approximations for calculating the implied volatility using the genetic programming approach. Applying our approximations to experimental data sets we can show that the genetically determined formulas outperform other formulas presented in the literature.