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I was reading this definition: https://investorplace.com/2018/08/what-is-implied-volatility-concern-investors-invtlk/

If its IV stands at 20%, a movement of 20%, or $20 per share, over a 12-month period would be equal to one standard deviation.

So then why do 1 DTE options have 80% IV at say \$320 strike on spy when spy is at \$386. Using that definition this means that a movement of 80% or \$308 per share over a 12 month period is equal to one standard deviation.

But intuitively. This OTM 1 DTE will almost never be ITM. So why is IV 80%?

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I hope it's clear that implied volatilities cannot and should not be interpreted as estimates of future stock price volatility -- apart from anything else, every strike will have a different implied volatility, whereas there is only one value for the expected realized volatility.

That still leaves the question of why the near-term out of the money put has much higher implied volatility than other options. There are a few things to consider --

  1. The time to expiry gets complicated for short-expiry options. For example, on Thursday morning before expiration date the stock will be a 1DTE (one day to expiry) and implied vol calculated as such, but there are two full day sessions and an overnight session before expiry, so this is really more like a 1.5 or 2 day to expiry option. If there is news expected between now and expiry (e.g. nonfarm payrolls on Friday morning) then there is even more volatility packed into this time period than usual so it might have a price reflecting an option with 3 or 4 days to expiry -- but implied vol is still calculated as if it has one day left (this tends to result in higher implied vols for near-expiry options).

  2. The Black-Scholes model is based on normally distributed stock returns, whereas real stock returns are negatively skewed and have fatter tails, especially on short time scales. This is reflected in a higher implied vol for near-expiry and out-of-the-money options, especially puts.

  3. Implied volatility is correlated with stock returns. If the market falls it is very likely that implied volatility will rise so the put option will become doubly more valuable (another way of saying it is that out of the money puts have negative vanna). This is reflected in a higher implied vol for puts than for calls, at least for equity index options.

  4. Implied volatility is stochastic, and option prices are not linear in implied volatility. In particular out of the money options increase faster than linearly as implied volatility rises, and part of the implied vol premium is to account for this (another way of saying it is that out of the money options have positive volga).

Remember that implied volatility is just a way of turning an option price into a number that can be more easily compared across different options on the same underlying. Don't think of it as a forecast of future realized volatility and you'll be fine.

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    $\begingroup$ Great answer. +1. $\endgroup$ – Jan Stuller Feb 10 at 9:04
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In the option pricing framework, one starts with a model for the underlying stock. In the Black-Scholes model, the stock price follows a geometric Brownian motion $$dS(t)=S(t)(\mu dt+\sigma dW(t))$$ where $\mu$ and $\sigma$ are two input parameters. From here, we can derive the price of, for example, a call option, and it turns out that the price of a call option at time $t$ depends on the following parameters: underlying price $S(t)$, risk-free interest rate $r$, strike $K$, time to maturity $\tau$, and volatility $\sigma$ (assuming no dividend). Notice that the option price does not depend on $\mu$, but it does depend on the volatility of the stock $\sigma$. Mathematically, call option price is a function of the 5 input parameters, and we can show that this function is increasing in $\sigma$. All this is hypothetical - indeed you know $S(t)$, $r$, $K$, $\tau$, and you can come up with an estimate of the volatility $\sigma$ from historical stock returns, but if you go on to the options exchange and take a look at call option prices, you will likely see that the theoretical prices you computed for different strikes do not fall in the bid-ask ranges for most, if not all traded options. Why is it so? One way to look at this is that suppose I am looking at a call option with 1 month to maturity, what I really need is the volatility of the stock during the future 1-month period, while the estimate we have is on historical prices. Thus, the price of this 1 month option in a way reflects market's expectation/view on the volatility in the coming month. Now what exactly is this "expected" volatility? Note that option price is a function of the input parameters, and it is increasing in the parameter $\sigma$ This means we can invert this function and back out a volatility $\sigma_{imp}$ such that if we put in this volatility into the option pricing formula, we get a price that agrees with the market price. This is the implied volatility - it is the volatility implied by the market price. If you do this to compute the implied volatilities for call options with the same maturity but different strikes, you will likely see that they are not the same - typically OTM and ITM options have higher IV than ATM options, a phenomenon called volatility smile (sometimes it is a skew instead).

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"why do 1 DTE options have 80% IV at say 320 strike on spy when spy is at $386"

80% IV is simply the vol consistent with the option price and other inputs. One to look at it is sellers don't want to sell wings too cheap hence high vol on very short-dated options.

"a movement of 80% or $308 per share over a 12 month period is equal to one standard deviation"

But it doesn't have 1y to expo. Perhaps better to think about this on a breakeven basis.

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