Oct 13, 2013

Volatility is Back – Now What? Capturing the Dynamics of Stochastic Volatility

Watch the Video: Capturing the Dynamics of Stochastic Volatility

Despite the ongoing budget debate in Washington equity indexes haven't dipped as low as the market might have expected. Characterized by some as a bull market, or at least a period of relative stability, recent events have also driven the VIX sharply higher. Recognized as the best gauge of fear in the market, as the VIX continues to surge, Numerix experts discuss what modelers and Risk Managers need to be thinking about in terms of model selection and best practices in the valuation of derivatives in order to capture the VIX dynamics of today.

Weigh in and continue the conversation on Twitter @nxanalytics, LinkedIn, or in the comments section.

Video Transcript: Capturing the Dynamics of Stochastic Volatility

Jim Jockle (Host): Hi welcome to Numerix Video Blog. I'm your host Jim Jockle. With me today, Tom Davis, Ph. D., Vice President of the Client Solutions Group here at Numerix. Tom how are you?

Tom Davis (Guest): Good, thank you Jim.

Jockle: Thank you for joining us. Over the past couple of months it's been pretty stable out there and one could argue that it's been a bull market. But given recent events, we've seen a wide upswing in the fear index and that means volatility is back.

Tom, I want to sit and talk to you. Just in the past couple of weeks and clearly as it relates to news of the potential for the U.S. to default on its debt, we've seen a very quiet VIX, sitting around sixteen, jump up to twenty, now sitting today around – back down to fifteen. In terms of modeling, as it relates to the valuation of derivatives, give us a little background on what should modelers be thinking about in terms of model selection and best practices as volatility is coming back into the market place

Davis: We see the dynamics in the VIX over the past couple of weeks. There's a couple of interesting things I want to talk about but definitely we need to ensure that our models for the markets, capture this stochastic volatility and the dynamics stochastic volatility.

Usually in the past, when you look at the VIX, versus the S&P, you see a strong negative correlation almost -.6 or so, which means in down markets you have more volatility. What's really interesting in the past couple of months that we see a very flat S&P, but yet as you say the volatility it seems to be jumping up with the VIX. And one of the hallmarks of the Heston Model, which is the stochastic volatility model, is this mean reverting feature of the VIX, of the volatility. And actually we see that. As you said it jumped up and then later when the markets didn't correct downward, the volatility index came back to its mean reverting behavior.

Jockle: So under the assumption that there's robust model valuation within internal departments as it relates to OCC guidelines, that have come out around model validation, what kind of testing should people be looking at and with what kind of regularity at this point of time. With the potential that this could just be a hiccup if everything goes back to normal within the U.S. But what kind of testing should people be looking at?

Davis: Definitely looking at historical back testing which means how did your different models perform over different periods of time you look at different things like what models best in prices, what models best by normal markets and at this point it's still not a crisis market. So when you do your model validation for your volatility models, for now, you should be looking at normal market behavior and looking at your option prices and your volatility and how it did track in your hedging portfolios, how they did track throughout the normal market conditions.

Jockle: And what would facilitate a change. I mean clearly external events. But is there something within the correlation because we aren't such a weird uncorrelated market between the S&P and the VIX. At what point should we be looking at changes?

Davis: Right. One thing with the model is, I'd like to say that if you ever observe any observable in the market you will find it to be stochastic. So one thing that we don't put into the modeling right now is the correlation. You can put in the term structure. Which means you can monitor or predict how the correlation can change over time, however that is not a stochastic variable.

The Heston Model is a two factor. So, it's not really under consideration to make the correlation stochastic but one thing for sure is that you should test your models with different levels of correlation. Traditionally we always put out a negative so just to see how your model reacts when it comes up to uncorrelated behavior like we're seeing now. You'll always see the mean reverting behavior. So that has to be a hallmark of your model when you do your validation.

Jockle: Tom I want to thank you so much for the insight. And you know what, as this progresses let's keep an eye on the correlation and keep this conversation going because lord only knows when we are at another point in change.

So follow along. We want to hear what you have to say and talk about the topics you want to talk about. Please feel free to join us and follow us on LinkedIn and back us on twitter @nxanalytics. And please feel free to connect with Tom on LinkedIn, or myself, to stay on top of all the information that we put out to into the market. With that, I'm Jim Jockle have a good day.        

Blog Post - Apr 13, 2010

LIBOR Market Models for Smile-Dependent Exotics

Need Assistance?

Want More From Numerix? Subscribe to our mailing list to stay current on what we're doing and thinking

Want More from Numerix?

Subscribe to our mailing list to stay current on what we're doing and thinking at Numerix

Subscribe Today!