Why does implied volatility vary with option strike price?

Why Does Implied Volatility Vary With Option Strike Prices?

In this specific example, a call IV goes up as the strike price goes down, but sometimes the IV is higher at both extremes, deep in the money and deep out of the money.

As you know, you are describing the volatility smile, the extremes in price IV for options that are deep in-the-money. You know from any graphical representation of the smile that as the strike prices move at a rate of change or Delta from its spot (current) price, the skewness of the tails sharply rise. This appears to correlate with the way options are priced, accounting for both intrinsic value and time value.

Let's Simplify

Options that trade out-the money (OTM), which is below the strike price for calls and above the strike price for puts, have no intrinsic value. Any premium price is strictly time value, which is the value placed by the market as it heads to expiration. At-the-money options should trade as spot contracts as they are pinned – strike price of the option and the market price of the underlying asset are 1:1.

Any premium, again, would strictly be time value based on market expectations for out-of-the-money options. This exposes a short writer to pin risk because any slight movement in-the-money just prior to expiration may result in exercise against and potential loss (or diminished gain). The volatility risk involved with each potential Delta can be measured by another options Greek, Vega. Vega can explain, in part, how at different strike prices IV will vary.

All options will revert to the mean at expiration, that is, to become nothing for OTM options, if not exercised. The further a strike price moves from spot means that the IV of the underlying asset must become greater in order to meet the expectation of the writer who is out-the-money. You wouldn’t sell a IBM call @60 when the market price is $75, nor would you sell a MSFT put @45 when the market for MSFT is at $50. These two out-the-money positions would certainly trigger an exercise as they would be advantageous to the holder.

The IV however comes into play when the Vega for long (positive) and short (negative) positions corresponds with a rise and fall in IV. Long calls and puts gain in a rising IV, which are the extremes of the smile, while short calls and puts gain from a falling IV, as strike prices move closer to spot.

Here’s a link to a nice, more comprehensive explanation of the volatility smile from Stanford University with more of the mathematical justification.

I think it’s important to appreciate how even the slightest changes in IV can reek havoc on our expectations to profit. But taking small, manageable positions that are not far from spot may be a better way to profit from more of your options trades without increasing volatility risk as measured by Vega.

One last important subject to touch on. Why then do we usually see higher IV in put options vs. call options? Fancy math aside, this can be explained more simply with trader emotions. Puts usually demonstrate higher IV than calls because the market is usually more fearful than greedy. Perhaps you have heard the adage, “The market takes the stairs up and the elevator down”. We see higher IV on put options as traders are more fearful that an OTM option could be realized for a loss if volatility explodes.

How to relate this to something tradable? For our users of the Brutus Options Ranker, we generally recommend it is better to sell put options than initiate a buy-write position (buying stock and simultaneously selling an OTM call). The margin requirements and profits are both generally more favorable with short puts vs. covered calls.

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