Square-Root Diffusion

The third stochastic process to be simulated is the square-root diffusion as used by Cox,

Ingersoll, and Ross (1985) to model stochastic short rates. Equation 16-5 shows the

stochastic differential equation of the process (see also Equation 10-4 in Chapter 10 for

further details).

Equation 16-5. Stochastic differential equation of square-root diffusion

We use the discretization scheme as presented in Equation 16-6 (see also Equation 10-5 in

Chapter 10, as well as Equation 10-6, for an alternative, exact scheme).

Equation 16-6. Euler discretization for square-root diffusion (full truncation scheme)

The Simulation Class

Example 16-5 presents the Python code for the square_root_diffusion simulation class.

Apart from, of course, a different model and discretization scheme, the class does not

contain anything new compared to the other two specialized classes.

Example 16-5. Simulation class for square-root diffusion

DX Library Simulation

square_root_diffusion.py

import numpy as np

from sn_random_numbers import sn_random_numbers
from simulation_class import simulation_class

class square_root_diffusion(simulation_class):
”’ Class to generate simulated paths based on
the Cox-Ingersoll-Ross (1985) square-root diffusion model.

            Attributes

            ==========

            name    :   string

                            name    of  the object

            mar_env :   instance    of  market_environment

                            market  environment data    for simulation

            corr    :   Boolean

                            True    if  correlated  with    other   model   object



            Methods

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            update  :