I can calculate the "Implied Beta" using implied volatility for the option stock, and implied volatility for the market (VIX). Is there any way to calculate also the correlation without performing a statistical analysis on historical data.

$\beta = ({\rho \sigma_{aapl}\ \sigma_{sp500}})/{\sigma_{sp500}} $

I know about the "Implied correlation" but this is the average correlation for all the stocks with the S&P500. I would the correlation for that particular stock


1 Answer 1


The simple answer is no. You need historical data to backuo the implied correlation.

A smart way to do it is to use Buss and Vilkov (2009) methodology.

Denote the risk-neutral correlation between each pair of stocks: $\rho_{ij,t}^Q$. The presence of the correlation premia led Buss and Vilkov (2009) to estimate the risk-neutral correlation by making: \begin{equation} \rho_{ij,t}^Q=\rho_{ij,t}^P-\alpha_t(1-\rho_{ij,t}^P) \end{equation}

Combining the above equation with the identifying restriction that equates the the observed implied variance of the market index $(\sigma_{i,t}^Q)^2$ with the calculated implied variance of a portfolio of all market index constituents $i =1,...,N$: \begin{equation} (\sigma_{i,t}^Q)^2=\sum_{i=1}^{N}\sum_{j=1}^{N}w_iw_j\sigma^Q_{i,t}\sigma^Q_{j,t}\rho^Q_{ij,t} \end{equation} one can solve for $\alpha$ and consequently get $\rho_{ij,t}^Q$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.