27
votes
Is the VIX more similar to a volatility swap or a variance swap?
\begin{align*}
\text{Variance strike} &= \mathrm{E}_t \left[ \int_t^T \sigma_u^2 du \right ] \\
\text{Volswap strike} &= \mathrm{E}_t \left[ \sqrt{\int_t^T \sigma_u^2 du} \right ] \\
\text{VIX}...
- 4,958
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 \...
- 14k
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 ...
- 1,487
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 ...
- 2,453
9
votes
Why is the VIX futures market usually in a state of contango?
VIX is a measure of volatility -- something that changes explicitly with uncertainty. The chances of uncertainty arising tomorrow, is lower than the chances of uncertainty increasing in the longer ...
- 91
9
votes
Accepted
Why is the VIX futures market usually in a state of contango?
Your questions about contango in VIX futures have close analogies in
options too. The Black & Scholes model suggests that all time
frames and all strikes should have the same implied ...
- 106
9
votes
Why is the VIX futures market usually in a state of contango?
Your question is an important one, but I am not aware of any particularly satisfying answer. There are several papers on this issue -- see Luo and Zhang 2009 and Zhang et al 2010, just for example.
...
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9
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 ...
- 469
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).
- 5,638
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 ...
- 171
7
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 ...
- 2,158
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 ...
- 14k
6
votes
Why is the VIX futures market usually in a state of contango?
VIX futures tend to rise when the S&P 500 falls -- the correlation of returns is about -0.7. If there were no contango in VIX futures, everyone would buy them to get free insurance against stock ...
- 552
6
votes
Accepted
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}{...
- 14k
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
- 341
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
...
- 9,617
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), ...
- 9,617
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 ...
- 14k
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 ...
- 5,853
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 ...
- 27k
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 ...
- 14k
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
Accepted
VIX options historical data
Unfortunately, there is no publicly available reliable source for historical VIX options data. Also, probably, in addition to VIX options you may need corresponding underlying futures data to do ...
- 946
5
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 = \...
- 1,856
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 ...
- 162
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 ...
- 96
4
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]
- 61
4
votes
VIX Futures data: why happen to have settle price > 0 and Volume = O.I. = 0
CFE calculates settlement price from quotes whether there was trading or not. "The daily settlement price for each VIX futures contract will be the average of the final bid and final offer for the VIX ...
- 2,453
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