Overview
The Bernoulli Model of Pd can be used to simlulate default.Bernoulli Distribution
The simplest way to simulate a default over a given time frame is to model the default as a Bernoulli variable. (see the Bernoulli Distribution). A Bernoulli variable is a random variable that takes only one of two values, with probabilities p, and (1-p).In the case of default, one could label default of asset i in a portfolio as
{% Default = D_i %}
Then the probability of default is labeled {% PD_i %}
Implementation
A simple way to simulate a 0-1 event such as default is to simulate a number from 0 to 1 with a uniform distribution, and if the simulated number is less than the probability of default, then take that as a default, otherwise take it to be no default.
//probability of default
let pd = 0.01;
let di;
let u = Math.random();
if(u<pd) di=1;
else di = 0;
Bernoulli API
The bernoulli module can also be used to simulate default.
let bl = await import('/code/bernoulli/v1.0.0/bernoulli.mjs');
//probability of default
let pd = 0.01;
let di = bl.random(pd);