Implied Volatility, Equity Skew, and the Leverage Effect
Summary
The document explores whether implied volatility represents the market’s expected volatility, why volatility often rises as equity prices fall, and why out-of-the-money puts tend to have higher implied volatility than calls. One answer notes that near-the-money options with short maturities can relate to risk-neutral expected integrated variance, while the connection weakens for longer maturities, options farther from the money, or when risk-neutral expectations differ from real-world outcomes. Another answer emphasizes that implied volatility is a way of expressing option prices in volatility terms, not a direct forecast.
The volatility rise during equity declines is described as an empirical pattern often modeled through negative co-movement between spot and volatility shocks, known as the leverage effect. The put skew is linked to demand for crash protection, which can raise put prices and their implied volatilities. These patterns are not universal: the answers distinguish equities from some other assets and note exceptions among single stocks and short expiries. The discussion is explanatory rather than a test of predictive performance.
Key ideas
- Implied volatility expresses an option price in volatility terms and is not automatically a reliable forecast.
- Near-the-money, short-maturity implied variance can relate to risk-neutral expected integrated variance.
- Equity volatility often rises as prices fall, a pattern associated with negative spot-volatility co-movement.
- Demand for downside protection can make out-of-the-money puts more expensive and raise their implied volatility.
- Equity volatility and skew patterns may not hold for other assets or every stock and expiry.
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Full text
# existence of implied volatility # existence of implied volatility I read a book where it was written : 1/ "implied volatility is the market's consensus on the volatility of the asset between now and the maturity of the option". -> Could someone explain me this sentence ? How can we arrive at this conclusion ? 2/ "if an asset drops in price, this is generally accompanied by an increase in it's volatility" -> Is this a fact of the market, an observed property ? 3/ and further : "this is reflected in the IV of the OTM puts being higher than the OTM calls because puts pay on the downside" This sentence is for me weird. If someone could explain me ? Tx a lot ! ## Answer by Kiwiakos (score 3, accepted) https://quant.stackexchange.com/a/25921 - You can show that "the implied variance of an ATM short maturity option is equal to the expectation under the risk neutral measure of the integrated variance over the life of the option." As you move away from the assumptions: ie not ATM, longer maturity, risk neutral measure far from true, then the forecasting power diminishes. (Google 'stochastic volatility ghysels harvey renault') - It holds for stock indices as an empirical observation. Not any asset. There are models that capture it through dynamics, eg negative correlation between spot shocks and vol shocks (leverage effect). - Put option are an insurance against bad states of the world (ie stock market crashes). Therefore market participants are willing to pay a bit more for them (buyers) or are more reluctant to write them (sellers). The outcome is a higher option price, which is reflected by a higher IV. ## Answer by user29970 (score 1) https://quant.stackexchange.com/a/25920 1 is wrong. The implied vol is a convenient way to look at the option price, nothing more. 2 is an observed fact for equities in general but not the case for some other assets eg commodity futures. 3 is also an observed fact for equities generally (but not for single stocks with short time to expiry). If 1 and 2 were true, then 3 would naturally follow. If we use a local volatility model (where instantaneous vol is a function of the stock price) then the shape of the local vol (from statement 2) would determine the shape of the implied vol (statement 3). ## Answer by Allen Maxwell (score 0) https://quant.stackexchange.com/a/25940 Implied Volatility means the option is overpriced versus the model price. It means I'm paying more to buy an option than normally. For example, when a gap happens on the stock, the option price is high. It has no bearing on what will happen, but more on what did. The Bid and Ask price are set by people with expectations. And those prices are out of line with "normal" due to some recent move and expectation. I teach Day Trading and have built software for this. It's not a prediction. It's a mistake (distraction) to treat it as a prediction. This is what traders want (Ask). As a writer of contracts, it would be risk and possible reward. Still gets back to using something else as confirmation of a trend. The night before Earnings announcements there are often big price increases for the 2 weeks leading up to that day. These are expectations again and reflect risk to the writer. However, in my research, 9 out of 10 options are NOT worth while to buy the high imp vol options. The 1 that works doesn't pay for the 9 that failed. Being a seller is statistically better, but if one that goes off is like recent GOOG or AMZN, selling a naked option is very expensive.
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