Was this is the best Bloomberg Quant Seminar? Here was a summary
Thanks to Sholom for sending
Professor Jim Gatheral Speaks about Fractional Volatility Models
– Use Fractional Brownian Motion to model SP500 Realized Variance
– The different of the logs of realized variance are gaussian
-The Hurst number is used as a degree freedom.
Just like a Student t distribution describes SP500 returns over time
by varying the degrees of freedom n (n=100 for low volatility environments and n=1 for very high volatility environments)
-For the really spiky parts of the realized variance distribution, the Hurst Number is set to .14 giving a very jumpy infinitely discontinuous function that is still measurable so you can use Lebesgue Integration to compute the sum over the high volatility time interval of Fall 2008.
– The open question is how to predict what hurst number to use at what time interval which would make the model predictive/forward looking instead of just descriptive.
Nassim Taleb started a huge fight with Jim claiming that the model
makes no sense since realized variance is not gaussian even when you compute the difference of the logs. Jim responded with the change in hurst numbers from 0.5 (random walk) to 0.14 (extreme discontinuous jumps). Nassim then made a comment about Rational Expectations which Jim agreed with. I think Nassim was
saying that you can’t predict huge jumps, so you remove them from
your predictive model and only include the extreme jumps as part of your descriptive model.
Extreme Modeling vs Rational Expectations:
Nassim Taleb seems to always think in terms of extreme events
(i.e. black swans induced by exogenous information). Jim Gatheral
took a more Rational approach by saying omit the extreme events since they are rare and you can’t predict them. Once you protect
yourself from black swan events, then use a model that predicts
all other types of events (driven by endogenous information)
to form the basis of your trading strategy
Best Bloomberg Lecture so far!!
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