Training dataset for exponential Ornstein-Uhlenbeck volatility model¶
The model is defined by the following equations
$$ dX_t = X_t \left( \mu dt + \exp(Y_t) dW_t \right) $$$$ dY_t = \alpha (m - Y_t) dt + \beta d \hat Z_t $$$$ \hat Z_t = \rho W_t + \sqrt{1-\rho^2} dZ_t $$with $X_0 = 1$ and the risk-free rate $r = \mu = 0$.
We use then the notations presented in the paper Mean-Reverting Stochastic Volatitity, IJTAF, 2000 by J-P FOUQUE et al.. In particular, the values of $\beta $ are defined through the expression $\beta = \sqrt{2\alpha \nu^2}$ where, in our simulations, we choose $\nu = \nu_{paper} (1-\exp(m)) $ with $\nu_{paper}$ is the one defined in the reference above.
The generated dataset represents the price of a call option for many choices of model parameters as well as for 256 combinations of the couple time to maturity "Tmt" and strike "Str". The values of these prices are obtained with Monte Carlo simulation of an Euler scheme that discretizes the Stochastic equations above. For this Monte Carlo simulated expectations, the number of trajectories is equal to $10^5$ and the discretization time step is equal to $\frac{1}{12*64} \approx 0.0013$
This training dataset can be downloaded from this link.