Rough Volatility European Call Calculator
Posted by Gary Pai
This calculator follows the Monte Carlo pseudo-code in rough_vol_with_pseudo_code.pdf. It prices a vanilla European call under the rough fractional stochastic volatility (RFSV) model by generating fractional Brownian motion paths, evolving log-volatility, and simulating the correlated stock path under the risk-neutral measure.
Model equations
\( dY_t = \left(r - \frac{1}{2}\sigma_t^2\right)dt + \sigma_t\,dW_t^S \)
\( dX_t = \nu\,dW_t^H - \alpha(X_t - m)dt,\ \text{with}\ X_t = \log \sigma_t \)
\( d\langle W^S, W^H\rangle_t = \rho\,dt \)
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.
Tagged: Rough Volatility, RFSV, Monte Carlo
• First Version: Sep 21, 2026 •
• Last Edited: Sep 21, 2026 •
Methods
Derivatives Markets
- Stock Options
Including Exotic Options - Interest Rate Derivatives
Short Rate Model - Credit Derivatives
structural Models and Reduced Models