Hi, I tried to price a vix options using stochastic model (Heston with garch) and black& scholes. whereas, I am not able to find the same figures as market prices ( call @21 ; mat : 08/17/2011 ; vix : USD 31,66 My price : 10,74 Market : 5,5 (last price; 08/05/2011) Volatility comes from Garch analysis and feeds model parameters. I downloaded the FED rates and vix daily prices n(instead vix futures) Current variance (GARCH) 0,004938 Times 0,033333333 Historical vol 6,92% Long terme variance 0,48% Whereas, I am not very sure about my calculation. Have you any ideas to improve my model and keep it more accurate regarding market figures ? Thanks for your help
How about try using VIX future price as underlying rather than VIX index value? FWIW, VIX futures are less volatile than VIX itself and reflects more on market's projection of what VIX will be come expiration day.
VIX options are not like other options. The underlying is a computed quantity (the VIX) not an asset that can be bought or sold. Market makers can not hedge with the VIX nor does put-call parity hold with respect to the VIX. So the usual pricing arguments do not hold. However, market makers can hedge with VIX futures, and put-call parity does hold with respect to the VIX future that has the same expiration as the options. So... instead of using the value of the VIX as the underlying price, use the price of the VIX future with the same expiration as the option. Then your formulas should come closer to giving a sensible answer. However, the price behavior of the VIX does not look like the price behavior of a stock. So option models designed for ordinary assets will at best give a crude approximation to the VIX option prices. Pricing VIX options is a special case of its very own.