Thursday, September 24, 2020

It is the Markov condition

PRICING THE TERM STRUCTURE OF VIX FUTURES
The term-structure of VIX futures contains interesting information on broker-dealer risk appetite. This is because, during risk-offs, dealers bid up the price of insurance against market volatility (which is what the VIX measures) but they only do so at the short end. That is, they bid up VIX futures with short tenors. This is why the term-structure inverts (called backwardation) when volatility spikes. This is clear from the surface plot of VIX futures prices (x is date, y is tenor and z is price).

The broker dealers are removing the skew under the assumption that money cannot be modeled. A sort of hybrid Black-Sholes and Markov.

They model the short end for the simple reason that the betting structure is finite binomial  when all the information is shared about events in the past. So all they need to do is match the slope at the left end of a binomial. The rest of the binomial takes is cue from the short end. So the broker/dealers remove skew, they are doing 3-tuple Markov.

The key to understanding all this is to know the past is ex post.  Because it is ex post, all trades are betting the complete cycles, from peak to peak.  Thus, the sequence in the past is recast as a binomial probability because they all have to bet each other as well as the past. It is self sampled systems.

The curve inverts because central bank money is a distortion, it is fouled with implied tax collection. Alpha is the first binomial, beta the second, and the broker-dealers create the third binomial for skew. gamma I think.  Matching moments, I see a lot of research on the topic these days.


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