A Proposed Model for VIX Derivatives Pricing

A Proposed Model for VIX Derivatives Pricing

The VIX may be about to get some competition. VIX is the “fear gauge,” the very visible measure of expected price fluctuations in the S&P 500 index options. On the foundation of its popularity, CBOE has built a monopoly on exchange-traded volatility products.

VIX derivatives have become among the most actively traded contracts at the CBOE, in part at least because they expose investors directly and efficiently (without the need for delta hedging) to volatility that is negatively correlated with stock returns.

So, a challenge to VIX, an alternative index for volatility, is big news. And that is precisely the news from Miami, where the MIAX is about to debut options on the SPIKES Index. SPIKES is based on underlying options, on the SPDR S&P 500 ETF Trust. VIX is calculated on out-of-the-money S&P 500 options. Since both are S&P based, then, it is unsurprising that their moves are parallel.

SPIKES was created by T3 in combination with BATS Global Markets back in 2016, through it has taken the founders the intervening three years to find an institution willing to tie traded options to it.

Scholarly Synchronicity

At this moment of impending competition, it is perhaps fortuitous that a professor at Rutgers Business School, Peixuan Yuan, has proposed a new model for understanding the pricing of VlX derivatives, one that he calls a “general affine jump-diffusion model.” This means that the proposed model allows for contemporaneous jumps in both VIX level and VIX variance, with the jump intensity to be governed by a persistent separate factor.

There have been several models proposed to address this issue, ever since there has been an VIX options market. But most of these models have failed to incorporate important features of the empirically observed markets. For example, the dynamics of VIX illustrates a very low correlation between the level and the shape of skew. The correlation between short-term implied skew and at-the-money vol is only 0.0832 in their levels and it is negative (-0.0285) in their changes.

To accommodate such features, Yuan’s model incorporates what he calls “central tendency factors.” He distinguishes two of them: (1) level central tendency and (2) variance central tendency.

Yuan also discusses risk premiums, both for VIX index risk (VIRP) and for VIX variance risk (VVRP). He finds that, “although the term structures of both risk premiums are negative and downward sloping, with inversion occurring around market crisis,” they reflect different risks. The VIRP is “the expected profit to a long position of the hypothetical futures contract which settles on the squared VIX.” The VVRP, on the other hand, is “the expected payoff to the long side of a variance swap of VIX futures.”

From VRP to VIRP

Earlier research on the analogous premium for stock returns, the VRP, has indicated that the premium is negative, on average, and that it can be used to predict stock returns. VIRP holds information similar to that embedded in VRP, but likely holds more of it, since the uncertainty of future conditional variance “partially overlaps with uncertainty about realized variance.” Why do investors willingly abide by a negative premium, i.e. a cost, of this arcane sort? Because they are “willing to pay the premium to hedge against future conditional stock variance fluctuations.”

The Yuan paper distinguishes between long-term and short-term VIRP. It finds that long-term VIRP is characteristically lower than the short-term VIRP, but with some convexity. That is: VIRP decreases as the time structure of the instrument becomes longer, until it reaches a minimum at the 120-day maturity. Then it starts increasing again.

The standard deviation of VIX shows concavity in its term structure. That is, the standard deviation increases as the maturity date gets further out, reaches a maximum at 60 days, then declines. This indicates a significant fluctuation in the mid-term VIRP.

VVRP and Jump Intensity

VVRP shows more dramatic variation over time than VIRP.

Yuan also discusses the “jump intensity factor” suggested by his model. He says the factor has become more important since the global financial crisis of 2008, because since then market participants have become increasingly afraid of “dramatic increases in either variance or variance of variance” and have become willing to pay more in order to hedge against them.

Be Sociable, Share!

Leave A Reply

← M&A Deal-Flow Faltering & Brexit is One Culprit Can LIBOR Be Replaced? →