Rough Volatility European Call Calculator

\( dY_t = \left(r - \frac{1}{2}\sigma_t^2\right)dt + \sigma_t\,dW_t^S \)

\( dX_t = \nu\,dW_t^H - \alpha(X_t - m)dt,\ \text{with}\ X_t = \log \sigma_t \)

\( d\langle W^S, W^H\rangle_t = \rho\,dt \)

The implementation mirrors the PDF structure: build the fractional Brownian covariance matrix, apply Cholesky decomposition, simulate rough-volatility paths, and discount the average terminal payoff from the pseudo-code simulation.

Leverage note: the PDF pseudo-code approximates the leverage effect by correlating the stock increment with the Gaussian innovations used to build the rough path. This page follows that same discrete-time approximation.

Notes: the page uses browser-side Monte Carlo simulation and the covariance-matrix construction is cubic in the number of time steps. Smaller values of N_steps and N_paths will return results faster. The long-run level \( m \) is the mean of log-volatility, not of volatility itself.