Estimating Implied Volatility Changes from Spot Moves

Summary

The exchange presents a regression-based way to estimate how implied volatility may change when the underlying spot price moves. It points to a minimum-variance delta relationship in which the expected implied volatility change depends on the proportional spot move, time to expiry, and a quadratic function of Black–Scholes delta. The coefficients in that function are estimated with ordinary least squares.

The method offers a practical model for mapping spot changes to volatility changes, but the excerpt does not give fitted coefficients, data requirements, or an accuracy comparison. Its estimates therefore depend on the calibration sample and fitted parameters, and the answer does not establish that one set of coefficients generalizes across assets or market conditions. It is a model-based estimate rather than a claim that volatility follows a fixed response to spot.

Key ideas

• A regression can estimate implied volatility changes conditional on spot moves.
• The proposed relationship uses proportional spot change, time to expiry, and a quadratic function of Black–Scholes delta.
• The coefficients are fitted with ordinary least squares.
• The excerpt provides no coefficients or evidence that the relationship generalizes across markets.

Tags

# change in implied volatility with respect to change in spot


# change in implied volatility with respect to change in spot












It's clear that IV increases as spot decreases, and vice-versa. In pricing an option, is there any model that is useful in estimating the change in IV with change in spot price?

For example, if the ATM for XYZ is priced today with IV of 0.1, and then tomorrow XYZ drops by 2%, how can I estimate the new ATM's IV? It certainly wouldn't still be 0.1.

What would be the simplest way to estimate this change? What would be the most accurate way to estimate it?

## Answer by emot (score 1, accepted)

https://quant.stackexchange.com/a/66193

In the paper "Optimal Delta Hedging for Options" link the author shows that the minimum variance delta is a function of change in implied volatility. If you use equation on page 9 i.e. $E[\Delta \sigma ]=(\frac{a+b \delta_{bs} + c \delta^2_{bs}}{\sqrt T}) \frac{\Delta S}{S}$ you will get what you want. The parameters a, b, c are fit with OLS regression.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.