Skip to content
All library documents

Spot–Volatility Correlation in the Heston Model

Article Quant Q&A · Author: EpicAdv
Read the original

Summary

The note addresses the observed tendency for asset prices and volatility to move in opposite directions, asking which volatility models can represent that relationship. It identifies this as spot–volatility correlation and explains that the Heston stochastic volatility model can capture it: setting a negative correlation between the Brownian shocks driving the asset price and its variance implies a negative relationship between price and variance.

The discussion points to a model feature rather than presenting a calibration method, derivation, or empirical test. It offers no parameter estimates or evidence that the relationship holds across markets or periods. The observation about SPY and VIX motivates the question, but the responses do not analyze that data. The practical takeaway is that return–volatility dependence can be represented through correlated price and variance shocks in Heston; model choice and the strength or stability of that dependence require further investigation.

Key ideas

  • Spot–volatility correlation describes dependence between an asset price and its volatility.
  • The Heston model can represent negative price–variance dependence through correlated Brownian shocks.
  • The sign and magnitude of the shock correlation are modeling choices that need appropriate estimation.
  • The note provides no empirical validation or calibration guidance.

Tags

VolatilityDerivatives pricingStatistics
Full text
# Are there volatility models dependent on returns?


# Are there volatility models dependent on returns?












When I look at the relationship between volatility and price, I see a clear negative correlation as shown in this figure (SPY and VIX prices today looking back 1 year).

The common volatility models (GARCH, Heston, etc.) do not seem to exploit this correlation. I'm sure they exist, but I just haven't found them. Can anyone point me towards models that do?

## Answer by Ruse (score 3)

https://quant.stackexchange.com/a/50648

The Heston model can have that property. If you make the correlation negative between the Brownian motions in the $dS_{t}$ process and the $d\nu_{t}$ process you imply that price is negatively correlated with variance.

## Answer by roz (score 2)

https://quant.stackexchange.com/a/50646

Yeah this is often called Spot-Vol correlation and is well known. Most people take this into account. I think if you just google spot-vol correlation you will come up with many example/models.

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.