Magazine article Modern Trader

Understanding VIX Futures and Options

Magazine article Modern Trader

Understanding VIX Futures and Options

Article excerpt


Although most traders are familiar with the VIX, many are perplexed by the unique unconventional relationship of its futures and options.

Greeks Volatility Skew

Since the Chicago Board Options Exchange (CBOE) introduced futures and, subsequently, options on its Volatility Index, or VIX, traders have asked why the contracts don't necessarily track the underlying in the same way other equity futures track their indexes. Others may wonder why the putcall parity is violated for VIX options. Then, there are the options that trade underwater, the vastly different implied volatilities for each expiration cycle and the question of arbitrage between S&P 500 derivatives and VIX contracts.

Thankfully, all of these questions can be answered with theoretical research on VlX futures and options pricing and, along the way, can offer guidance to some practical applications of these products. Our findings also apply to recently launched VSTOXX index futures and options listed on Eurex,

While the value of the VIX, which is generally accepted as a broad measure of market volatility, is derived from prices of S&P 500 index options, it is not simply a weighted sum of underlying options (unlike other equity indexes like the S&P 500, where the index is a weighted sum of component prices). The options from which VIX is calculated sum up to the square of VIX, not VIX itself. This non-linear transformation means that you cannot just buy or sell a basket of options whose expiration price equals the index. Because of this non-linear component, there is no way to statically replicate the VIX.

Because the underlying VIX is not tradable, the futures on the VIX are not tied by the usual cost of carry relationship that connects other indexes and index futures. To price the futures that have no tradable underlying, we must follow a statistical approach based on various factors: the distribution of the VIX, the strength of the trend, meanreversion and volatility. In a sense, VIX futures are much like options, having their own set of Greeks.

Close relationship

The first and most obvious attribute of VIX futures is that their options can be priced off the futures using the BlackScholes futures options formula. Putcall parity holds and is observed in the market, but it is the put-call parity with the futures contract as the underlying, not the VIX index. In-the-money options do not trade in discount to their intrinsic value when calculated off the futures.

The futures chain forms a curve that "connects" the current value of the index with its long-term expectation. To simplify: When the VIX is above its long-term mean, the futures chain will likely be in backwardation, and when the VIX is below its long-term mean, the futures chain will likely be in contango. However, the chain does not need to be strictly decreasing or increasing; it can be completely flat, concave, or convex.

The futures and options tend to anticipate moves. If the VIX has made a sharp move up and traders expect it to come down before expiration, futures will trade below the index, and calls will seem relatively cheap. On the other hand, if VIX is low and traders expect the index to revert to some higher level before expiration, futures will trade above the index, and calls will seem relatively expensive. Theoretical models provide quantitative explanation of these features.

The VIX index and futures are connected by a statistical relationship that depends on how fast the VIX tends to move toward its average level, the volatility of the index and how much time is left until expiration. Near expiration, the futures will be close to the index and move in tandem with it, while the longterm futures reflect the long-term expectation of VIX plus risk premium.

VIX futures have a dynamic relationship with the index, just like options are related to their underlying stock by delta. Traders know that VIX futures do not always follow the index. …

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