Implied Volatility of Volatility Index

Today I noticed a very interesting phenomena. While CBOE Volatility Index $VIX.X was falling, its call options were actually rising in price.

For anyone who is somewhat familiar with the definition of calls, this would make very little sense. Call options are the financial instruments that derive their value from the underlying product. They give the right to the holder to buy underlying product at a set price (strike price). If current price of the underlying instrument is higher than the strike price, the owner can simply buy the underlying instrument at a set price and unload it at the market price. (This is very simplistic explanation and is not advisable to act upon. Options have embedded time value and should be sold, rather than executed before the expiration).

Getting back to $VIX.X – on 11/02/09 it closed at 29.78 and on 11/03/09 it closed 28.79. Meanwhile, I hold +VIXLF – VIX December Call Options with strike price 30. Yet, the price of my call option has risen to 2.45-2.55 from yesterday’s 2.35 level. How could that be?

If you received your MS from NYU Courant Institute in Math in Finance, as I did (or a similar program at a few other universities), you know the answer. If not, below it is.

Have you ever heard about Black-Scholes Option Pricing Model? For 3 semesters most of my classes were centered around this model one way, or the other. Every single interview I had on Wall Street consisted of Black-Scholes model questions.

So, what is that model? It’s like a secret soup recipe If you put bunch of ingredients in the pot and cook it, you’ll get the price of the option (soup). (SORRY, I don’t cook much, but I had so much theoretical math, that I can come up with the theories in any life dimensions). The price of the underlying instrument is just one of the ingredients; there is also time to the expiration, risk-free interest rate, strike price, volatility and the cooking procedure (functions). If you know all the ingredients you can guess how the soup will taste. If you tried the soup, you can guess the ingredients. If you put too much salt – the soup is salty, if the soup is salty, it’s fair to assume that there was too much salt put in.

Now, on the left side of the equation we have decrease in the spot price, on the right side – increase in the option price. Working back through the model, we deduce that Implied Volatility of the underlying instrument has increased. What is “Implied Volatility”? It’s market opinion about future volatility.

Let me repeat this one: In Market opinion, future volatility of the Volatility Index will increase. Or to make it digestible – market expects a big move.

Look at the following chart of Dow Jones Industrial Average:

This technical analysis may explain why even good news can’t pull DJIA higher in the last few days.