VIX futures spreads

A short post on practical pricing VIX futures curve with application to trading futures spreads. Here is the VIX futures curve based on Friday's (latest at the time of writing) settlement price, and prices from 1 week ago. Market up, VIX futures down, some aberrant settlement values in November that we should not focus on. 

The raw prices from futures are difficult to work with, so the term structure is converted to a functional space - that is we find a function that can represent all kinds of futures curves. There is no "simple regression" approach that can work for raw prices as futures time to maturity changes from minute to minute, but in a functional space that is possible. The solid lines in the chart above are not simple connections between the dots - they are the theoretical values of the futures curve, the functional projection I wrote about. 

In this functional form we can create forecasting models that predict how the term structure will evolve from one time period to the next. 

The uncertainly in the forecasting model can be projected back into the price space, and the resulting confidence intervals have financially intuitive properties - they are not symmetric around the forecast, and confidence intervals have their own term structure: wider near expiration, and narrower for back months. 

 As well as simulate individual scenarios, which is important.
The distribution of individual scenarios are important for trading spreads. Even if uncertainly on individual futures leg modeled using some "nice" approximation, the two legs are nonlinearly correlated, and the expected PL from a spread is skewed. In the example below based on the most recent data I plotted the distribution of short April long May spread. The expected PL for the next trading week is almost 0 in this case, but it is clear that the legs do not move in parallel.

If they moved in parallel, then predicted prices would like on the 45 degree line ( in grey dashes ) . Also there is skew although the chart does not show it well.

How will my forecasts turn out? We'll find out next week. 

If you are interested in my work - I am looking for a full time job, or a consulting opportunity, and my email is on the right-side bar.

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