Hi, I was wondering if there was any relationship, between implied vol and time-to-maturity, found in the market place in general or for specific assets? I cant seem to find anything too good online. For example, would the implied vol ATM differ for a 1 month option vs 1 year option?(holding all other contract specifications constant) thanks!
In equity options, typically the longer dated options have lower implied vols. Commodities can be different. For example, look at the implied vol for GLD which follows gold. The back months are always higher except during big short term moves. The exception for equity options is at times of very low vols or during holiday periods.
I believe what your talking about is called the term structure of volatility. There are a few good papers on this site regarding how to analayze and trade it. http://www.ssrn.com/
In equity options, longer dated options tend to have a higher implied volatility. This is the term structure of vol where there is more uncertainty in the future than now. When things get crazy the term structure becomes inverted and the longer dated has a lower implied vol than the shorter dated. This is because the market starts to believe the that current uncertainty will have a resolution in the future.
So you are saying that the IV increases with the maturity T in the normal market condition and decreases with T in crazy times like financial crisis?
Here is a simple graph for SPY IV VS Days to Option Expiration that may provide some insight. (current data) Note that the X-axis is log scale to properly show the relationship with time.
As shown in the fact that vix is typically in contango and gets inverted in very volatile times .. Basically showing the mean reverting nature of volatility.. Good thread... Another nuance is the very high number vol number shown very near expiration.. Which is more a function of convexity effects as gamma exponentializes near expiration.. Leaving otm options extremely convex to price... It's like the price of vol with no time to revert to any mean
https://en.wikipedia.org/wiki/Volatility_smile Note the 3 dimensional model. For short 210 put on spy: Exp................Vol Aug...............13.1 Sept..............15.5 Oct................14.2 Dec...............16.4 Jan '16..........15.7 Mar...............17.0 Jan '17..........18.5 Div in Sept, Dec, etc.
I really like that 3-d graph, as it conveys a lot of information. Typically, this "future ripple" in that graph is due to an upcoming event, such as earnings, while one would not expect such a "future ripple" in SPY or IWM unless Janet Yellen, for example, has a scheduled announcement or something similar. The "sometimes common" volatility smile, is an attribute of the volatility variance over the range of strike prices at a given time to expiration at a specific point in time. A 3 dimensional view which includes both time to expiration, and each strike produces what is often referred to as the "volatility surface", which is a 3-D representation of IV at a specific point in time. The IV values I used in the graph above omit the influence of strike price variations to try to keep the focus on the original question regarding ATM option IV VS time to expiration, buy choosing a specific IV for each expiration. Note: For SPX, the VIX number is the 30-DTE value. For RUT, the 30 day IV number would be the RVIX. I am still learning, and looking to see how close one may be able to reproduce the Volatility Surface for SPX and RUT options from VIX and RVX respectively. I suspect such approximation may have some value, when one does not have access to the individual option IV. Below, I am pasting the source data for the various expirations I used in the simple graph for reference (I only used a subset of these). This is from TOS. Please note, my current interest is with indexes, such as SPY/IWM, etc, so the observations for specific stocks, such as AAPL may vary greatly.