Forward Variance and Parameters in the Rough Heston Model

Summary

The document asks why rough Heston calibration or neural-network approximation may use the Hurst parameter, correlation, volatility of volatility, and forward variance, while leaving out mean reversion, initial variance, and long-run mean variance as separate inputs. Its answer points to a relation from a paper on hedging in rough Heston models. The relation connects a time-dependent input to the expected variance path and the initial variance, with mean reversion also appearing.

The suggested argument is to substitute this relation into the original model and take the limit as mean reversion goes to zero. This indicates a way to express or simplify the variance-related parameters through forward variance. The response is brief and does not show the substitution or resulting formula, so it offers little detail for checking whether the parameterization is equivalent in the setting asked about. It also gives no calibration results or neural-network evidence.

Key ideas

• The question concerns representing rough Heston inputs through forward variance rather than separate variance-level parameters.
• The answer cites a relation involving expected variance, initial variance, and mean reversion.
• It proposes substituting that relation into the model and taking a zero mean-reversion limit.
• The response omits the derivation and does not establish equivalence for every parameterization.

Tags

# Forward variance in rough heston model


# Forward variance in rough heston model












When calibrating or trying to approximate the rough heston model by a neural network, why is it done according to the hurst parameter, the correlation, the volatility of volatility and the forward variance, when in the definition of the model, the speed of reversion, initial variance and the mean variance to which it reverts to are also parameters, why do we encapsulate these three in the forward variance ? is it equivalent ?

## Answer by Zelin Wu (score 1)

https://quant.stackexchange.com/a/78922

Refer to the paper Perfect hedging in rough Heston models, there is a relation

$$ \lambda\theta^0(t) = D^{\alpha+1}(E[V_t]-V_0)+\lambda E[V_t] $$

After substituting this formula into the original rough heston model and letting $\lambda$ being zero, you fill find the right formula

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.