Out of three probabilistic approaches, simulations provide the most complete assessments of risk.

• Better input estimation. They are based upon probability distributions for each input, rather than a single expected value or discrete outcomes.
• Output: a distribution for expected value. The output from a simulation takes the form of an expected value across simulations and a distribution for the simulated values.

Some common constraints introduced into simulation:

• Book value constraints. The book value of equity means little by itself. The book values of many firms are significantly different from their market values.
  • Regulatory capital restrictions. Banks and insurance companies are required to maintain certain book value related ratios.
  • Negative book value for equity. Simulations can be used to assess this probability and protect against it.

• Earnings and cash flow constraints. These constraints can come from internal or external sources. Simulations can be used to assess how likely they are to be violated and the impact.
• Market value constraints. Simulations can be used to model distress and measure indirect bankruptcy costs.

Key issues:

• Garbage in, garbage out. Deep understanding of statistics concepts is also required.
• Real data may not fit distributions.
• Non-stationary distributions: parameters such as mean and variance may change over time.
• Changing correlation across inputs.