Black-Karasinski Model
=======================

.. automodule:: torchquantlib.models.interest_rate.black_karasinski

.. autoclass:: BlackKarasinski
   :members:
   :undoc-members:
   :show-inheritance:

   .. automethod:: __init__

   .. automethod:: simulate

   .. automethod:: _apply_constraints

Class Methods
-------------

__init__(a_init=0.1, sigma_init=0.01, r0_init=0.03)
    Initialize the Black-Karasinski model.

    :param float a_init: Initial value for mean reversion speed.
    :param float sigma_init: Initial value for volatility.
    :param float r0_init: Initial value for short rate.

simulate(S0, T, N, steps=100)
    Simulate interest rate paths using the Black-Karasinski model.

    :param float S0: Initial asset price (not used in this model, included for consistency).
    :param float T: Time horizon for simulation.
    :param int N: Number of simulation paths.
    :param int steps: Number of time steps in each path.
    :return: Simulated interest rates at time T.
    :rtype: torch.Tensor

_apply_constraints()
    Apply constraints to model parameters to ensure they remain in valid ranges.