Monte Carlo Simulation in Finance

Introduction

• Monte Carlo simulation is a widely applied finance technique.
• Used to deal with uncertainty in complex situations.
• Generates many random observations for uncertain variables to create a joint distribution of possible outcomes.

Steps in Monte Carlo Simulation

1. Determine Variables
   • Identify variables representing sources of uncertainty.
2. Assume Distributions
   • Choose a distribution for each variable.
   • Choice of distribution affects model predictions and is at the analyst’s discretion.
3. Execute Iterations
   • Perform iterations with possible realizations for these variables.
4. Repeat Iterations
   • Repeat the 3rd step many times (hundreds to thousands).
   • Observe a large number of possible realization paths.
   • Determine the mean of the distribution.

Applications in Finance

• Options and Derivatives Pricing Models
  • Useful when complex features are involved.
• Company Valuation
  • Cross-check results obtained through a Discounted Cash Flow (DCF) method.
• Risk Management
  • Used for Value at Risk (VaR) estimation and volatility modeling.

Advantages

• Leveraged by advancements in computing power.
• Allows analysts to gain insights into possible realizations from a given distribution function.
• Helps estimate possible prices of an asset by testing different variable values.

Drawbacks

1. Model Dependency
   • Results depend on the assumed distribution model.
2. Statistical Nature
   • It's a statistical approach rather than an analytical one.
   • Provides aggregate results, not detailed impacts of separate variables.