Finite Difference Models

All Finite-Difference Models (one factor) include a common section (FD), and a model dependent section. The common section has the following parameters.

• TIMESTEP: The incremental timestep of simulation (in years).
• MAX_X: Distance of the upper (or lower) boundary of the model grid from the center.
• N_X: The number of levels from the center, in each direction.

e.g.

"FD": {
    "TIMESTEP": 1 / 250,
    "MAX_X": 0.1,
    "N_X": 250,
},

Black-Scholes Model

qablet.black_scholes.fd.BSFDModel

In the Heston model the lognormal stock process $X_t$ is given by,

$$dX_t = (\mu_t - \frac{\sigma^2}{2})dt + \sigma dW_t$$

The model specific component in the dataset (BS) is a dict with VOL ($\sigma$), and the name of the asset:

e.g.

"BS": {
    "ASSET": "SPX",
    "VOL": 0.3,
}

Hull-White Model

qablet.hullwhite.fd.HWFDModel

In the Hull White model, the short-rate follows the following process. $$dr_t = [\theta_t - a r_t]dt + \sigma dW_t$$

The model specific component in the dataset (HW) is a dict with the parameters:

• $a$, the mean reversion rate (MEANREV).
• $\sigma$, the volatility (VOL).

e.g.

"HW": {
    "MEANREV": 0.1,
    "VOL": 0.03,
}