John Yang

And not to mention the expected value and volatility.

Looking at recent events, the volatility is through the sky.

And that is not something that would have happened in the last decade.

After doing all of these, the final output that we are getting is a thousand simulated paths and each of them covering 80 years of returns.

Through our testing, we see that our results have preserved more realistic, higher order distribution features.

For example, skewness and kurtosis.

For listeners who are not familiar, skewness simply means the distribution is not perfectly balanced or symmetric.

And kurtosis means extreme events in the tails.

Essentially, we're looking at the tails.

If you look at the comparison graph on the right of the slide, the newly simulated distribution using our method are compared with the historical behavior, the historical empirical CDF, the cumulative distribution of the return and the Gaussian baseline that PWL was using before.

You can see that the new method followed a historical shape more closely, especially in the left tail where the Gaussian model is way too smooth.

That's the benefit of using the empirical structure.

We're not forcing it into any of the shape.

It's the same as running a optimizer.

Like when you're trying to optimize, there are constraints that's stopping you from getting that exact shape that history has showed us.

And not just visually, we've also ran tests on it to look at how big the improvement has been comparing to the Gaussian baseline.

We believe at the end of the day, the goal for us is not to produce a more complicated model.

Rather, we want something that's actually usable.

So we look at three things.

First, we look at if each acycline simulator return pattern look more realistic.