Meaning of IV for a strike

Question

As I understand it, IV is defined as an annualized 1 standard deviation range for an underlying. So what is the meaning of implied volatility for a strike?

1. The IV on each strike is calculated by inputting the market price of the option into the Black-Scholes model. If the pricing model calculates IV per strike, how do you get a value for the underlying as a whole? For example Tastyworks says that for January expiration SPY has an IV of 21.7%. Is this an average or other aggregation type formula that combines IV from all the strikes? Is there such a standard formula or do other trading platforms it differently?

2. For example the 250 put on SPY is 20 points out of the money and has a 23.76% IV. Does this mean that someone buying the 250 put for the current market price is valuing the volatility for this cycle at 23.76% and say someone else buying the at the money put (270 with 18.7% IV) for the current market price is valuing the volatility for this cycle at a lesser value?

Answer 1

Historical Volatility is the standard deviation of daily price changes, not Implied Volatility.. It's the most commonly used determination of HV but there are other methods as well.

I have never seen a calculation of the Implied Volatility for a strike. There can be several options at the same strike or as many as 3 dozen (the heavily traded SPY). Each option has its own implied volatility and it is calculated as you wrote in paragraph 1).

Different web sites calculate the Average Implied Volatility in different ways. Some just average the different IVs. Some do more complex calculations (IVolatility which uses a proprietary weighting of the delta and vega of 4 ATM options per expiration. If you really want a headache, read about the calculation of the CBOE Volatility Index (VIX).

Some brokers will provide an IV per option, an average IV per expiration, and an average IV for the stock (all options).

Options of the same expiration can have very different values. A volatility smile is when the IV of each option is higher as the option gets further out-of-the money. There are also Option Smirks (IV has either a Forward or Reverse Skew).

Answer 2

As I understand it, IV is defined as an annualized 1 standard deviation range for an underlying.

That's incorrect. That definition is for Historical Volatility, which is not the same as Implied Volatility (or IV).

what is the meaning of implied volatility for a strike?

Implied Volatility is one of the parameters of many option pricing models. Simplifying:

call price = f(underlying price, strike, time to expiration, dividends, risk-free rate, implied volatility).

For a given option (say, call) contract, you know strike and time to expiration by the contract definition. You know call price by looking at the market. You know dividends and underlying price by looking up information about the underlying stock. You know the risk-free rate by tracking treasuries rates. The only unknown is implied volatility. So you can solve the equation and find the IV.

That is the definition of IV.

1. how do you get a value for the underlying as a whole?

There's no standard definition of "the IV of the underlying", nor "the IV of the underlying for month X". You'd have to ask your broker to know exactly which definition they are using. I don't know what Tastyworks use.

It's typical to follow the definition of the VIX, so you can look that up on the Cboe website.

2. Does this mean that someone buying the 250 put for the current market price is valuing the volatility for this cycle at 23.76%

Not exactly - like mentioned before, there's no such thing as "the volatility for this cycle"; at least not as a standard definition. What's happening is that the market is pricing that 250 Put at 23.76% implied volatility -- in other words, 23.76% is the "magic number" that is found by solving the equation defined by the option pricing model you are using.

The difference in IVs that you mention is very common in the marketplace - it's commonly referred to as volatility smile. There's no single explanation for the phenomenon.

One common explanation is the fact that market returns are not normally distributed - there are fat tails - while option pricing models typically assume normal or log-normal returns.

The fat tails mean that prices jump really far more often than predicted by normal distributions. If the IV of OTM options was the same as ATM options, those OTM options would be underpriced - that is, the buyer of those options would have a positive expected return. But the marketplace prices contracts in a fair way, otherwise arbitrage opportunities would exist. That's why IV is higher for OTM contracts.

Answer 3

There are both implied volatilities for each option price (volatility smile) and for each expiration (term structure). These 2 dimensions combined create the "volatility surface".

The underlying's IV is usually done vix style, which is simply the expiration iv closest to the 30 days. Pull up any stock's option chain, look at the expiration closest to or on 30 days. In ThinkOrSwim, it will show you the iv for that expiration. This number will be the same or very similar to the iv shown for the underlying stock.