Does low implied volatility mean all options for that underlying are cheap, or just the near-term options?

Question

I understand how implied volatility works, but the one aspect I am unclear on is whether all options for an underlying move together as implied volatility changes. For example, I have seen the implied volatility at a one-year low for near-term options, yet the longer term options are somewhat higher (40% instead of 30%, for example). How does this actually work?

Answer 1

Implied volatility is determined by the supply and demand for options. If market makers get a lot of orders from people wanting to buy options, but relatively few from people wanting to sell options, they will increase the IV of their bid and ask quotes. If they get more sell orders than buy orders, they will decrease the IV of their quotes.

Usually IV is fairly close for all options with the same expiration date for any given underlying.

IV is likely to be higher for a far month than the near month when there are no events (earnings releases, FDA new drug approvals, etc.) expected before the near month expiry. Since stock prices usually change for a reason, traders who do not expect there to be any reason for the stock price to change before expiry also expect volatility to be lower, making buying the near term options less attractive.

Similarly, if an event that is expected to have a major impact on the stock price is expected before the near month expiry the near term options may have a higher IV than longer term options.

As for your original question, remember IV is a property of options, not the underlying. If I said "IV is low for the options on stock XYZ" I would probably mean all options, but I would not assume that if someone else said that he would mean the same thing. He might be talking about only near term options.

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I see since I originally answered Mr. Simpson has taken exception to my answer. I want to let you know I stand by my answer.

I will agree with him that vega will be higher for an option with a longer time until expiration, but that is not what you asked. You asked about implied volatility.

If you want an example of IV being lower for a longer-term option, check out the different IV values for AGIX.

Mar07 - 212%
Apr07 - 242%
Jul 07 - 227%
Jan08 - 183%
Jan09 - 183%

I obtained the IVs using the basic options calculator at

http://www.ivolatility.com/calc/

for the $12.5 strike.

Traders are expecting AGIX to receive a new drug approval letter within months, inflating the nearer term IV.

I also strongly disagree with the statement "If you are comparing options on two different stocks that are identical in every way, except for the volatility of the underlying asset, then for any given expiration, the option on the low volatility stock will always be cheaper than the option on the high volatility stock." IV is based upon projections of future volatility and those projections do not always correspond to historical volatility. An obvious example of this is when a company has accepted a cash take over offer, but it has not yet been voted upon by the stockholders. Assuming the take over offer was for 20% more than the price of the last trade before the takeover was announced, that would probably have caused a big jump in the historical volatility of the stock while simultaneously causing a big drop in the implied volatility.

If you want confirmation, I suggest ask again on the Yahoo Futures and Options message board at

http://messages.yahoo.com/Business_%26_Finance/Investments/forumview?bn=4686677

where some (ex) market makers participate.

Answer 2

Do not listen to anything that zman492 says. It is completely wrong on so many levels.

Mathematically, your are asking if the second partial derivative with respect first to volatility and then time to expiry is positive. Or more simply, holding all else constant, how does the vega respond to increasing time to expiration?

The short answer is that it is increasing. Thus, the IV for a 5 year option is greater than that of a 1 year option, etc, etc, etc.

To prove it for yourself, pick your favorite closed form, continuous time option pricing model- such as Black-Scholes. Find the first derivative with respect to volatility- this is the vega. Next differentiate Vega with respect to time to expiration. You Will discover that for a given set of values, that the vega is increasing in time to expiration.

You can also show the same result with a discrete time model such as cox-ross-rubinstein or hull-white.


Another way to answer your Q:
If you are comparing options on two different stocks that are identical in every way, except for the volatility of the underlying asset, then for any given expiration, the option on the low volatility stock will always be cheaper than the option on the high volatility stock.

Answer 3

Check out Black-Scholes.

The following is the formula for the price of a call option with exercise price K on a stock currently trading at price S, i.e., the right to buy a share of the stock at price K after T years. The constant interest rate is r, and the constant stock volatility is σ.

C(S,T) = S\Phi(d_1) - Ke^{-rT}\Phi(d_2) \,