VIX options pricing model

Anyone knows what model is used to price VIX options?

Clearly not Black-Scoles since the underlier returns are not log-normal.

Tried fitting a Black-Scoles to it and was completely off, of course. So question is what is it?

 

Are you using the index itself or the VIX futures as the underlying?

 

I guess the VIX futures. From a pricing point of view you need to replicate the option with the underlier and since in this case the index is not directly trade-able, you need futures in replication. So I expect a pricing model to take this into account.

 

In that cause you should be able to use Black76 as a model unless you're doing something fancy like trying to extract relative value.

 

Hmm, I'll check, thanks.

 

thats not gonna work. is your Google broken?

 

Dude, you are being childish. I know you love fancy models but you also have to understand that practical applications do not require them most of the time.

Like any futures, VIX futures contract is a martingale under Q measure. So you totally can use Black76 model to price and risk-manage options on VIX futures, as long as you understand the limitations of the vol-of-vol numbers. Granted, the deltas are going to be a bit wacky because of the jumps included in the vol and you have to be mindful of the vol ramp-up (a.k.a the Samuelson effect). However, simply using black volatilities backed out of the market prices and applying some simple rule of thumb corrections is going to be sufficient for most applications, including market-making.

 

I won't argue with that, you are right.

 

The problem with using black76, for you, is that the underlying last price you get from your data vendor (DeltaNeutral aka HistoricalOptions, StrickNet...) is from the VIX index itself, not the relevant futures. So to price off of the futures you would have to, in your nightly process, treat VIX as a special case and merge in futures closing data, a coding complication you may not have time for. A better solution is to price VIX, and all other index options, off the implied forward, which is easily calculated without having to do a left join on another table. The other advantage to this is that you don't have to choose between close,settle, or bidask mid for your futures input (Friday VX1216 bidask = 24.45 24.50, close = 24.375, settle = 24.46).

Any model (bsm. black76...) will "fit" the a current options price -- just plug in the right vol number. But you really aren't interested in the price, but rather the greeks, so that you can hedge properly. Black76 greeks may be off, so smooth your price curves (put and call) and get delta, gamma, etc from taking numerical derivatives from those curves.