Structural Model
================



This module implements a structural model for credit risk calculation.

Functions
---------

.. autofunction:: structural_model

Detailed Description
--------------------

The `structural_model` function implements a structural model for credit risk assessment. This model is used to calculate the probability of default and other credit risk metrics based on the firm's asset value and debt structure.

The model uses the following key equations:

1. Merton model-based approach for credit risk assessment
2. Utilizes PyTorch for efficient GPU-accelerated computations
3. Supports both single-firm and portfolio-level risk calculations
4. Incorporates time-varying volatility and interest rates
5. Allows for custom debt structures and maturity profiles

Mathematical Background
^^^^^^^^^^^^^^^^^^^^^^^

The model uses the following key equations:

1. Asset value process:
   dV_t = μV_t dt + σV_t dW_t

   Where:
   - V_t is the firm's asset value at time t
   - μ is the drift rate
   - σ is the asset volatility
   - W_t is a standard Brownian motion

2. Default probability:
   P(default) = N(-d2)

   Where:
   - N() is the standard normal cumulative distribution function
   - d2 = (ln(V_0/D) + (r - σ^2/2)T) / (σ√T)
   - V_0 is the initial asset value
   - D is the face value of debt
   - r is the risk-free interest rate
   - T is the time to maturity

3. Credit spread:
   s = -1/T * ln(1 - P(default))

   Where s is the credit spread

Usage Example
^^^^^^^^^^^^^

Here's a basic example of how to use the `structural_model` function:

.. code-block:: python

    import torch
    from torchquantlib.core.risk.credit_risk.structural_model import structural_model

    # Set up parameters
    # [Add example parameters]

    # Calculate credit risk metrics
    # [Add example calculation]