S&P IV vs VIX

F

frostengine

What is the relationship between VIX and IV on S&P index such as SPX or SPY options.

For example, as you go further out in time the IV on the S&P options is higher, just like the VIX futures are higher. Does that mean that say for March SPX options, the IV is being priced off of the march VIX future vs spot VIX?

What is the actual relationship, such as an IV of 15% would correspond to a VIX future of x?
 
VIX is roughly equal to 1 month vol at 25-delta strike. The slope of the futures curve is going to be steeper then that of implied vols since futures refer to forward variance. Trading one against the other is very tricky because of the variety of second order effects and other problems
 
sle said:
VIX is roughly equal to 1 month vol at 25-delta strike. The slope of the futures curve is going to be steeper then that of implied vols since futures refer to forward variance. Trading one against the other is very tricky because of the variety of second order effects and other problems
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Why the 25D is that because it'sa tepresentativeaverage of the strip... There is a premium to viz future ls due to the hedging costs associated with the fungible options strip... Strike risk etc
 
Lower delta is representative of the strip because the weights are calculated as inverse of square of the strike - so lower strikes have lower weight and implied variance (which is what VIX calculates) is higher then ATM if the skew is positive. 25-30 delta is just from experience.
 
frostengine said:
What is the relationship between VIX and IV on S&P index such as SPX or SPY options.

For example, as you go further out in time the IV on the S&P options is higher, just like the VIX futures are higher. Does that mean that say for March SPX options, the IV is being priced off of the march VIX future vs spot VIX?

What is the actual relationship, such as an IV of 15% would correspond to a VIX future of x?
More...

VIX is priced off of several S&P options, relating to the time to maturity of the VIX-future. So when maturity is 30 days, they use the 1 month options. Kinda... The VIX-spot is the expected 30 day variance, so equivalent to the 30 days to maturity options IV. They use an average of a few options IV's.
The 2-month VIX future is similarly calculated by taking the equivalent options series.
http://cfe.cboe.com/education/vixprimer/about.aspx.
 
JackRab said:
VIX is priced off of several S&P options, relating to the time to maturity of the VIX-future. So when maturity is 30 days, they use the 1 month options. Kinda... The VIX-spot is the expected 30 day variance, so equivalent to the 30 days to maturity options IV. They use an average of a few options IV's.
The 2-month VIX future is similarly calculated by taking the equivalent options series.
http://cfe.cboe.com/education/vixprimer/about.aspx.
More...
I have a few questions:

1. From reading the explanations of VIX off the CBOE website, seems like VIX represents the expected IV of the ATM calls/puts of 30 days maturity (using some sort of interpolation/extrapolation of actual IVs). To compare with actual volatility (historical) in 30 days, do I have to wait 30 days and calculate the standard deviation of the underlying price movement during those 30 days?

2. And how accurate is VIX representing 30 days IV?

3. Has anyone done that and see if there is indeed a risk premium and if so how much is the risk premium? In one of the threads, someone posted a study that claimed there is a consistent 3+% risk premium comparing VIX to historical volatility over the last couple of decades. A 3% IV premium for SPX can generate huge profits over time. Anyone done that type of trades and generated huge profits?

Appreciate your thoughts.

If any of you have any comments and thoughts, and if my interpretations of VIX is not correct, please do not hesitate to comment.

Thanks.
 
(1) No, VIX is a calculation of implied variance which is a weighted average of OTM option prices. IV is a BS model parameter while implied variance is model-independent (as it's a replication of log contract payoff) and it's connection to IV is only coincidental.

(2) See (1), it has very little to do with it. Practically, you will sometimes see ATM IV go down while variance stays the same and the other way.

(3) There is risk premium, but you need to remember that variance price includes HUGE convexity component. Your payoff is (RV^2 - K^2)/(2*K) as opposed to a volatility payoff being (RV - K). That means a vol spike has quadratic attribution to your P&L (i.e. know also as swift kick in the nuts).
 
sle said:
(1) No, VIX is a calculation of implied variance which is a weighted average of OTM option prices. IV is a BS model parameter while implied variance is model-independent (as it's a replication of log contract payoff) and it's connection to IV is only coincidental.

(2) See (1), it has very little to do with it. Practically, you will sometimes see ATM IV go down while variance stays the same and the other way.

(3) There is risk premium, but you need to remember that variance price includes HUGE convexity component. Your payoff is (RV^2 - K^2)/(2*K) as opposed to a volatility payoff being (RV - K). That means a vol spike has quadratic attribution to your P&L (i.e. know also as swift kick in the nuts).
More...
Thank you for your comments. Can you explain to a layperson what do you mean by:

"implied variance which is a weighted average of OTM option prices",

and how is it related to historical volatility as lot of folks used VIX as a proxy for IV. Also, why is important in volatility trading?

And what is convexity in variance price?

Regards,
 
sle said:
(1) No, VIX is a calculation of implied variance which is a weighted average of OTM option prices. IV is a BS model parameter while implied variance is model-independent (as it's a replication of log contract payoff) and it's connection to IV is only coincidental.

(2) See (1), it has very little to do with it. Practically, you will sometimes see ATM IV go down while variance stays the same and the other way.

(3) There is risk premium, but you need to remember that variance price includes HUGE convexity component. Your payoff is (RV^2 - K^2)/(2*K) as opposed to a volatility payoff being (RV - K). That means a vol spike has quadratic attribution to your P&L (i.e. know also as swift kick in the nuts).
More...

Ah, I didn't know that... How far of is impl varience? I do know that IV's are slightly of depending on the model you use.

Re (2), if ATM vol drop and wings go up... the strip might stay the same though and keep VIX at the same level.
 
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