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 \...
- 14.5k
13
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 ...
- 1,507
11
votes
Accepted
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 ...
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10
votes
Accepted
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 ...
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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).
- 5,798
8
votes
How is implied volatility derived?
For How VIX works you can read this wonderful blog : http://onlyvix.blogspot.com/2011/09/intuitive-understanding-of-vix-formula.html
It provide wonderful non mathematical explanation of the how ...
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8
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 ...
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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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}{...
- 14.5k
7
votes
Accepted
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 ...
- 14.5k
6
votes
Accepted
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 = \...
- 1,886
6
votes
How do market makers hedge VIX index options?
Due to the lack of a carry arbitrage, VIX futures are actually the direct hedge for VIX Index options
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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
...
- 10.6k
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 ...
- 14.5k
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
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 ...
- 51
5
votes
Accepted
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 ...
- 14.5k
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
votes
VIX options historical data
Interactive Brokers offers historical data for VIX options. You need to have an account , other than that - historical data downloads are available for no extra charge. You have to write some code to ...
- 51
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 ...
- 27.3k
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 ...
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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 ...
- 1,886
4
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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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 ...
- 101
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 ...
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4
votes
Accepted
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 ...
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