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16 votes

Pricing VIX Futures

Heston - Change of measure Consider the following Heston dynamics written under the real world measure $\Bbb{P}$ \begin{gather} \frac{dS_t}{S_t} = \mu_t dt + \sqrt{v_t} dW_S^{\Bbb{P}}(t),\ S(0) = S_0 \...
Quantuple's user avatar
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13 votes
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Derivation of VIX Formula

The piece you are missing is an approximation via the Taylor formula of the logarithm: $$\ln(1+x) \approx x-\frac{x^2}{2} \; .$$ Apply this to the first term in the final formula of the technical ...
Raskolnikov's user avatar
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11 votes
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Is the VIX more similar to a volatility swap or a variance swap?

The price/value of the VIX index is more akin to the strike/price of a variance swap expressed in vol units than to the strike/price of a vol swap. However, if you are to trade a VIX future (i.e. a ...
RAY's user avatar
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10 votes
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How was the old VIX calculated?

There were two changes to the VIX; the first change in 2003 that switched from S&P 100 options to S&P 500, and from implied volatility to variance swap method. The second change was in 2014 ...
onlyvix.blogspot.com's user avatar
9 votes

What does the VIX formula measure and how does it work?

The other answers have given a good qualitative description of what the VIX measures. In this answer, I will try to give a comprehensive quantitative overview of how the VIX formula works. What is the ...
Maximilian Janisch's user avatar
9 votes
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What is the appropriate benchmark for a Long/Short VIX futures strategy?

If your strategy truly has no directional bias, then the benchmark should be cash (ie whatever you would earn using the capital in your trading account and taking no risk).
Chris Taylor's user avatar
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8 votes
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Why not just be long VIX and wait for the next volatile period?

Put simply, VIX is a spot index (fair value to a variance swap on SPX of constant maturity) that you cannot own as a security. Market participants create futures for you to trade. Futures trade higher ...
ExIR's user avatar
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7 votes
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Risk, required return and expected volatility - what is the relationship?

I think you may be interested in this QJE forthcoming article by Ian Martin. The key idea of the article (page 5) is that the expected return on the market can be decomposed as $E_t[R_{t+1}]-R_f = \...
fni's user avatar
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7 votes
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Construction of VIX and VVIX

Strictly speaking, indices such as the VIX are built to approximate the expected variance (of log-returns) that would effectively realise under a pure diffusion setting (i.e. no jumps) $$ \frac{dX_t}{...
Quantuple's user avatar
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7 votes
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GARCH models vs VIX

These are 2 completely different ways of estimating volatility. GARCH models are calibrated on historical time series i.e. information provided under the real-world measure $\mathbb{P}$. Although you ...
Quantuple's user avatar
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6 votes

What is the appropriate benchmark for a Long/Short VIX futures strategy?

You could compare it, over the historical period of interest, to 1000 randomly generated VIX strategies which are: Flat on 60 Percent of days (randomly chosen days) Long VIX futures on 20% of days ...
nbbo2's user avatar
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6 votes

How many options would be required to dynamically replicate the VIX nowadays?

Gonzalez-Perez (2015) Model-free volatility indexes in the financial literature: A review makes some remarks on this topic in section 2.2. Andersen, Bondarenko & Gonzalez-Perez (2013) identify a ...
Martin Georg Haas's user avatar
6 votes

VIX OTM put options decrease value after sharp decrease of underlying

Yes, the VIX took a sharp downfall on 2020/03/02, from 40.11 to 33.42 (-6.69). But that is not what the 2020/04/15 Put options are based on, they are based on the 2020/04/15 VIX Futures (VIJ20), ...
nbbo2's user avatar
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6 votes
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Does shifting/scaling the IV surface relatively/absolutely introduce arbitrage?

Long story short: yes both might introduce static arbitrage opportunities if performed blindly. There are 3 types of static arbitrage to consider: Calendar arbitrage: total (implied) variance should ...
Quantuple's user avatar
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6 votes

Does fear or greed drive option prices?

Variance Premia; disentangled. Let me address this question a bit differently and bring the question forward: What part (i.e. 'side') of the volatility smile attracts a significant premium in ...
Kermittfrog's user avatar
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5 votes

How was the old VIX calculated?

The old VIX index is based on the Black-Scholes implied volatility of S&P 100 options. To construct the old VIX, two puts and two calls for strikes immediately above and below the current ...
vonjd's user avatar
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5 votes

VIX options historical data

Just for future visitors of this post: You can also buy VIX option data directly from the exchange where they are traded, the Cboe: [https://datashop.cboe.com]
teekanne's user avatar
5 votes

Why is the VIX futures market usually in a state of contango?

The fact VIX has a very large contango (right now a % carry of 10%/month) has to do with rational risk premium. The net supply of stocks is 1, so on net investors are long the stock market. They want ...
John's user avatar
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5 votes
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Does Bakshi, Kapadia and Madan (2003) VIX building approach underestimate volatility?

In your implementation, you are approximating continuous integrals over the strike domain by Riemann sums. This introduces an error. More specifically, for a fixed time to expiry $\tau$, you're ...
Quantuple's user avatar
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5 votes

What is the appropriate benchmark for a Long/Short VIX futures strategy?

If you are developing this strategy to use personally, I would benchmark it against your next best option. If the strategy has been developed to attempt to manage other peoples money I would ...
user89135's user avatar
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5 votes
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VIX lagging or leading indicator

In the sense it's derived from option prices and reflects investors expectation, it is a leading indicator. if nobody sees a market downturn in advance, then the option prices wont reflect such ...
ProbNerd's user avatar
4 votes
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How to compute 30/60/90-day Implied Volatility?

Thanks to @Quantuple I was able to modify the steps listed above to give a more accurate calculation. I'll run through the modified steps with real numbers all the way to the result. The process is ...
Chuck Remes's user avatar
4 votes
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Intuition Behind Scaling Factor in Variance Swaps

I believe you want to know why the VIX is a weighted portfolio of calls and puts with weights proportional to $\frac{1}{K^2}$ (NB: obviously the T is there to adjust for time to maturity, hence is not ...
fni's user avatar
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4 votes
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How did the SVXY ETF (-1x VIX) survive a 115% jump in VIX?

The CBOE VIX index is an aggregated spot value calculated from options. The index itself cannot be traded. Volatility ETPs are usually designed to track an underlying index on VIX Futures that is ...
He Shiming's user avatar
4 votes

How to hedge a short VIX position with SPY

Calculate the beta of the VIX Dec 18 contract to the SPY. Then apply this equation: $$\ hedge \ ratio = \frac{1000\beta}{SPY_{price} } $$ You then take the hedge ratio round it and that will ...
PlantFox's user avatar
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4 votes
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Futures short interests vs open interests

The Bloomberg ticker "CVXCTNCS Index" is the CFTC commitments of traders report for short positions of non-commercial traders, i.e. traders categorized by the CFTC as not having a commercial interest ...
Chris Taylor's user avatar
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4 votes
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Correlation Gold and SPX in BBG

I do not think that you were terribly wrong thinking that gold and SPX (or equity market in general) are negatively correlated. The reason behind this is that gold and stocks are in fact negatively ...
AK88's user avatar
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4 votes
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Relationship between VIX and Vega

Vega is the option's price sensitivity to the volatility (i.e. IV). In the graph below, vega is shown to be a strictly positive function in volatility, which means that at any point in the graph (i.e. ...
Jan Stuller's user avatar
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4 votes

Relationship between VIX and Vega

VIX almost always only spikes when SPX goes down as @Jan Stuller also mentions in a comment. Insofar the question is a bit counterfactual. I frequently use twin axis in the charts that follow. The ...
AKdemy's user avatar
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