**3. Research design and methodology**

Accurate volatility forecasting is an essential element in conducting good dynamic hedging strategies. The first thrust of this paper deals with generation of implied volatility from option markets using static and dynamic training of genetic programming, respectively. While the static training [8] is characterized by training the genetic programming independently on a single Sub-sample, the dynamic training allows the genetic programming to train on the entire data sub samples simultaneously rather than just a single subset by changing the training Sub-sample during the run process. This permits to improve the robustness of genetic programming to generate general models adaptive to all training samples. The second thrust of this paper is to study the accuracy of the generated genetic programming implied volatility models in terms of dynamic hedging. Since the true volatility is unobservable, it is impossible to assess the accuracy of any particular model; forecasts can only be related to realized volatility. In this paper, we assume that the implied volatility is a reasonable proxy for realized volatility, to generate forecasting implied volatility models using genetic programming and then to analyze the implications of this predictability for hedging purposes.

Figure 1 illustrates the operational procedure to implement the proposed approach.

**Figure 1.** Description of the proposed approach's implementation

The operational procedure consists of the following steps: The first step is devoted for the data division schemes. The second step deals with the implementation of genetic programming1 (GP), the application of training subset selection methods and the selection of the best forecasting implied volatility models. The last step is dedicated to dynamic hedging results.
