Normal-Inverse-Gaussian jump model

The model is defined by the following equations

$$ X_t = X_0 \exp \left( (\mu-w)t + \sum_{t_i \leq t} \Delta X_{t_i} \right) $$ $$ \Delta X_{t_i} = \sigma N_i \sqrt{ \Delta S_i} + \theta \Delta S_i $$ $$ \Delta S_i \sim \frac{\Delta t}{\sqrt{2 \pi x^3 \kappa}} e^{-(x-\Delta t)^2/(2\kappa x)} 1_{x>0},\quad N_i \sim \mathcal{N}(0,1) $$

with $X_0 = 1$, the risk-free rate $r = \mu = 0$ and $w = \left(1 - \sqrt{1 - 2 \theta \kappa - \kappa \sigma^2}\right) / \kappa$.

We use the notations presented in the book Financial Modelling with Jump Processes, Chapman and Hall, 2004 by R. Cont and P. Tankov. We also employ the same Monte Carlo simulation algorithms described in this book using discretization scheme with a time step of $\Delta t = 0.001$. The derivative prices are computed by simulating a large number of trajectories.

In addition to the information available in DataCarlo and AIvault, including details such as the name of each file to download, as well as the username and password, access to:

1. The neural network that generates the distribution of $X_t$ requires appending the file name to the URL

   "mlp.lpma.math.upmc.fr/" + "AIvault/NIG/Asset/"

2. The neural network that generates the derivative price value requires appending the file name to the URL

   "mlp.lpma.math.upmc.fr/" + "AIvault/NIG/Derivatives/"

3. The training dataset requires appending the file name to the URL

   "mlp.lpma.math.upmc.fr/" + "DataCarlo/NIG/Training/"

4. The validation/training dataset requires appending the file name to the URL

   "mlp.lpma.math.upmc.fr/" + "DataCarlo/NIG/Testing/"