How Spot Moves Relate to Equity Options Skew

# Skew spot relationship


# Skew spot relationship












How does skew : (25D Put Iv - 25D Call Iv)/50D Iv change with spot? Is there a well defined relationship? And why?

E.g does falling spot increase or decrease skew? How is that change is skew different across expiries (weeklies vs monthlies vs 3 monthlies) etc.

## Answer by KaiSqDist (score 1)

https://quant.stackexchange.com/a/80868

From What Does Implied Volatility Skew Measure? - Mixon (2011), it seems that the skew measure you are referring to is inversely related to the spot price (S&P 500 in this case). Take note that the skew measure in Mixon is continuous 30 days TTM (similar to the VIX).

See the figure below for a comparison between Figure 1 in Mixon (2011) and the VIX by CBOE for the duration of Jan 2005 to Jan 2010, which proves that both show a similar pattern and are thus inversely related to the spot (since VIX is well-known to be inverse to the S&P 500 and is used as a hedge for systematic risk ).

You can see that they both spike around the same time below.

## Answer by QuantCalc.net (score 0)

https://quant.stackexchange.com/a/85297

The short answer is no. There is no well defined relationship.

The options Skew (your definition) serves as a quantifiable measure of the asymmetry in the underlying asset's marginal probability distribution at the option's maturity.

In simple terms, it tells you whether the market is pricing a higher likelihood for a large move to the upside or the downside.

A Positive Skew (Put IV>Call IV) suggests that options hedging against downside risk are more expensive than options betting on equivalent upside gain. This indicates the market views the risk of a sharp drop as greater than the risk of a sharp rally.

Empirical Observation: Skew Stickiness (Leverage Effect) While the relationship is not a mathematical identity, empirical evidence shows a consistent relationship between the spot price movement and the skew:

- When the Spot Price Drops (↓): The skew becomes more positive (i.e., the price of puts rises faster than the price of calls). This steepening reflects increased fear and demand for portfolio protection.

- When the Spot Price Rises (↑): The skew flattens (becomes less positive or closer to zero). This compression reflects reduced fear and a decrease in the price of downside protection.

This inverse relationship is often referred to as skew stickiness or the leverage effect—the tendency for volatility to rise when the market declines and fall when the market rallies.

Beyond the Two-Point Measurement While the skew ratio is a useful snapshot, it is a simplification. The skew only captures the difference between two specific points (the 25-Delta Put and Call) on the broader volatility smile/smirk curve.

To truly understand the market's expectation for the underlying asset, one should analyze the entire volatility smile. The shape of the entire volatility curve can be inverted to derive the market's implied probability density function [Gatheral 2011]. This PDF gives a more complete picture of the market's expected probabilities for all possible prices at expiry, going far beyond just the two points used for the skew ratio.