2
$\begingroup$

I have a question about local volatility models.

In a lot of articles it is stated that the implied spot vol correlation of this model is -1 and we usually compare this with stochastic volatility models where you can control this correlation.

Is there a proof demonstrating how this correlation is -1 ?

I tried by computing the covariance and replacing sigma with Dupire formula but cannot find -1.

Thanks

$\endgroup$
1
  • 1
    $\begingroup$ In a LV model, inst. vol is a deterministic function of $S_t$, $\sigma_t = \sigma(t,S_t)$. Applying Ito you can then write $d\sigma_t = \cdot dt + d\sigma(t,S_t)/dS dS_t$. The target correlation (computed from the indiv quadratic variation and covariation) is then simply $\rho=\text{sign}(d\sigma(t,S_t)/dS)$. For equity markets that are negatively skewed, this usually yields -1 $\endgroup$
    – Quantuple
    May 7, 2022 at 9:44

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy