The proposed multifractal research workflow estimates model parameters from observed prices and then generates different synthetic paths with comparable statistical properties, rather than reproducing the historical path point for point.

groundsUntitled source

If you can distill the essence of GE stock behavior over the past 20 years, then you can apply it to financial engineering. You can estimate the risk of holding the stock over the next 20 years. You can estimate how many shares of the stock to buy for your portfolio. You can calculate the proper value of options you want to take on the stock. This is, of course, exactly the aim of all financial theory, conventional or not. The one difference, this time around, it would be nice to have an accurate model. To me, the greatest charm of the multifractal model is its economy. One simple set of rules can produce a great variety of behavior, depending on the circumstances. By contrast, most financial academics are going through a love affair with another way of modeling market volatility. Its main inventor, Robert F. Engel, shared a Nobel in 2003 for its development. It starts from some of the same facts I have been advancing in this book. Volatility clusters, due to dependence.

groundsUntitled source

More importantly, the multifractal model successfully predicts what the data show, that at short time frames prices vary wildly, and at longer time frames they start to settle down. Putting the model to work. but enough of theory. How do you use these ideas as a real-world financial tool? First, the equations need to feed into a computer model. The model must work two ways, forward and backward. Forward means that we should be able to construct artificial price charts from the fractal seeds, just as we did with the cartoons. Backward means that we should be able to take raw price data, analyze it on our computers, and estimate the key parameters that the multifractal model requires. Then, using those values, we should be able to tell the computer to reconstitute the market, to generate an artificial price series that differs from the real one, but follows the same statistical pattern.