Guest Post: A Qualitative Review Of Vix F&O Pricing As Well As Hedging Models

By Azouz Gmach

VIX Futures & Options are i of the close actively traded index derivatives serial on the Chicago Board Options Exchange (CBOE). These derivatives are written on S&P 500 volatility index in addition to their popularity has made volatility a widely accepted property cast for trading, diversifying in addition to hedging instrument since their launch. VIX Futures started trading on March 26^th, 2004 on CFE (CBOE Future Exchange) in addition to VIX Options were introduced on February 24^th, 2006.

VIX Futures & Options

VIX (Volatility Index) or the ‘Fear Index’ is based on the S&P 500 options volatility. Spot VIX tin displace hold upwardly defined as foursquare origin of xxx 24-hour interval variance swap of S&P 500 index (SPX) or inwards unproblematic terms it is the 30-day average implied volatility of S&P 500 index options. The VIX F&O are based on this spot VIX in addition to is similar to the equity indexes inwards full general modus operandi. But structurally they receive got far to a greater extent than differences than similarities. While, inwards illustration of equity indices (for illustration SPX), the index is a weighted average of the components, inwards illustration of the VIX it is amount of squares of the components. This non-linear human relationship makes the spot VIX non-tradable but at the same fourth dimension the derivatives of spot VIX are tradable. This tin displace hold upwardly amend understood alongside the analogy of Interest Rate Derivatives. The derivatives based on the involvement rates are traded worldwide but the underlying asset: involvement charge per unit of measurement itself cannot hold upwardly traded.

The dissimilar relation betwixt the VIX derivatives in addition to the underlying VIX makes it unique inwards the feel that the overall deportment of the instruments in addition to their pricing is quite dissimilar from the equity index derivatives. This also makes the pricing of VIX F&O a complicated process. Influenza A virus subtype H5N1 proper statistical approach incorporating the diverse aspects similar the forcefulness of trend, hateful reversion in addition to volatility etc. is needed for modeling the pricing in addition to deportment of VIX derivatives.

Research on Pricing Models

There has been a lot of query inwards deriving models for the VIX F&O pricing based on dissimilar approaches. These models receive got their ain merits in addition to demerits in addition to it becomes a tough determination to create upwardly one's heed on the close optimum model. In this regards, I let on the run of Mr. Qunfang Bao titled ‘Mean-Reverting Logarithmic Modeling of VIX’ quite interesting. In his research, Bao non only revisits the existing models in addition to run past times other prominent researchers but also comes out alongside suggestive models subsequently a careful observation of the limitations of the already proposed models. The basic thesis of Bao’s run involves mean-reverting logarithmic dynamics as an essential aspect of Spot VIX.

VIX F&O contracts don’t necessarily rail the underlying inwards the same means inwards which equity futures rail their indices. VIX Futures receive got a dynamic human relationship alongside the VIX index in addition to practise non just follow its index. This correlation is weaker in addition to evolves over time. Close to expiration, the correlation improves in addition to the futures powerfulness displace inwards sync alongside the index. On the other mitt VIX Options are to a greater extent than related to the futures in addition to tin displace hold upwardly priced off the VIX futures inwards a much amend means than the VIX index itself.

Pricing Models

As a volatility index, VIX shares the properties of hateful reversion, large upward jumps & stochastic volatility (aka stochastic vol-of-vol). Influenza A virus subtype H5N1 skillful model is expected to convey into consideration, close of these factors.

There are roughly 2 categories of approaches for VIX modeling. One is the Consistent approach in addition to the other beingness Standalone approach.

        I.            Consistent Approach: - This is the pure diffusion model wherein the inherent human relationship betwixt S&P 500 & VIX is used inwards deriving the aspect for spot VIX which past times Definition is foursquare origin of frontwards realized variance of SPX.

      II.            Standalone Approach: - In this approach, the VIX dynamics are guide specified in addition to thence the VIX derivatives tin displace hold upwardly priced inwards a much simpler way. This approach only focuses on pricing derivatives written on VIX index without considering SPX option.

Bao inwards his newspaper mentions that the standalone approach is comparatively amend in addition to simpler than the consistent approach.

MRLR model

The close widely proposed model nether the standalone approach is MRLR (Mean Reverting Logarithmic Model) model which assumes that the spot VIX follows a Geometric Brownian displace process. The MRLR model fits good for VIX Future pricing but appears to hold upwardly unsuited for the VIX Options pricing because of the fact that this model generates no skew for VIX option. In contrast, this model is a skillful model for VIX futures.

MRLRJ model

Since the MRLR model is unable to create implied volatility skew for VIX options, Bao farther tries to modify the MRLR model past times adding bound into the hateful reverting logarithmic dynamics obtaining the Mean Reverting Logarithmic Jump Model (MRLRJ). By adding upward bound into spot VIX, this model is able to capture the positive skew observed inwards VIX options market.

MRLRSV model

Another means inwards which the implied volatility skew tin displace hold upwardly produced for VIX Options is past times including stochastic volatility into the spot VIX dynamics. This model of Mean Reverting Logarithmic model alongside stochastic volatility (MRLRSV) is based on the aforesaid procedure of skew appropriation.

Both, MRLRJ in addition to MRLRSV models perform as good inwards appropriating positive skew observed inwards illustration of VIX options.

MRLRSVJ model

Bao farther combines the MRLRJ in addition to MRLRSV models together to cast MRLRSVJ model. He mentions that this combined model becomes somewhat complicated in addition to inwards furnish adds piffling value to the MRLRJ or MRLRSV models. Also extra parameters are needed to hold upwardly estimated inwards illustration of MRLRSVJ model.

MRLRJ & MRLRSV models serve amend than the other models that receive got been proposed for pricing the VIX F&O. Bao inwards his paper, additionally derives in addition to calibrates the mathematical expressions for the models he proposes in addition to derives the hedging strategies based on these models as well. Quantifying the Volatility skew has been an active expanse of involvement for researchers in addition to this query newspaper addresses the same inwards a really scientific way, keeping inwards sentiment the convexity adjustments, futurity correlation in addition to numerical analysis of the models etc. While farther validation in addition to dorsum testing of the models may hold upwardly required, but Bao’s run definitely answers a lot of anomalous features of the VIX in addition to its derivatives.

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Azouz Gmach plant for QuantShare, a technical/fundamental analysis software.

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