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 \...
- 14.8k
14
votes
Accepted
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 ...
- 1,537
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 ...
9
votes
Accepted
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).
- 5,971
8
votes
Accepted
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 ...
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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 = \...
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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
...
- 11.8k
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 ...
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), ...
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6
votes
Accepted
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 ...
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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 ...
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5
votes
Accepted
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 ...
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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]
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5
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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 ...
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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 ...
- 284
5
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 ...
- 1,910
5
votes
Accepted
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 ...
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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 ...
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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 ...
- 111
4
votes
Accepted
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 ...
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4
votes
Correlation Gold and SPX in BBG
Gold's "safe haven" credentials and its correlation to equities are not necessarily quite the same thing.
Gold is a safe haven, in the sense that whatever happens in the economy, an ounce will ...
- 5,141
4
votes
Accepted
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. ...
- 6,490
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 ...
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4
votes
The Holy Grail of Volatility Modelling: The SPX & VIX - Why?
Recall that the VIX can be expressed as a weighted portfolio of European call and put options on the S&P500. Thus, there is a relationship between the VIX and the S&P implied volatility, so ...
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3
votes
Accepted
Volatility Index for Industries
The VIX Index is computed from option prices on S&P Index.
A VIX-like Index for other industries would first require to have a liquid option market.
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3
votes
Replicating Log Contract - Errors Introduced by Jumps
The static replication result, i.e. a continuous strip of adequately weighted OTM vanillas can be used to replicate a variance swap, only holds:
under a pure diffusion assumption
if one considers ...
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3
votes
Does the correlation between stocks in an index affect the implied volatility of the index?
As Quantuple said, the variance of an index is related to the pairwise correlations $\rho_{ij}$ between stocks in the index
$\sigma^2_p = \sum_i^N\sigma_i^2w_i^2+2\sum_{i=1}^{N}\sum_{j>i}^N w_i\...
- 11.8k
3
votes
Accepted
Does the correlation between stocks in an index affect the implied volatility of the index?
Concerning your specific question:
Does the correlation between stocks in a sector or between sectors in the S&P 500 have an impact, all else equal, on the S&P's implied volatility / the ...
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3
votes
Accepted
How is VIX different from SPY/SPX IV?
What is your definition of SPX IV? ATM? ATM vol will be less than VIX. VIX is calculated by pricing a variance swap on SPX. A variance swap is priced theoretically using all strikes from 0 to ...
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