Monte Carlo Model: A Brief Guide

What is the Monte Carlo Model?

• The Monte Carlo Model is a system used in mathematical finance to calculate option prices. More specifically, the Monte Carlo method will calculate the value of a singular option with multiple sources of speculation and complexities.

• In regards to theory, the Monte Carlo Model utilizes risk neutral valuations; in this practice, the price of the option is shown as its discounted expected value. When applied, this technique will generate several thousand random price paths used simulate then subsequently calculate the associated exercise value or payoff of the option. These generated payoffs are then average and discounted on the specific trading day. The result of this 4-step process will yield the value of the option.

• In most cases, an option attached to an equity may be modeled with one source of uncertainty: the price of the underlying stock. For these options, the Monte Carlo is typically not utilized, for a more routine or simplistic pricing formula (Black Scholes) will suffice.

• The beauty behind the Monte Carlo model is that it allows for a compounding in the uncertainty of the underlying asset. For example, in a situation where the underlying asset is denominated in a foreign currency, an additional source of uncertainty will be found in the exchange rate. Thus, the exchange rate and the underlying price must be separately simulated and then combined to accurately determine the value of the currency. In models, such as the Monte Carlo Model, correlation between these sources of risk is incorporated. How is the Monte Carlo Model Applied?

• The Monte Carlo Model is most useful when valuating options that contain multiple sources of uncertainty or possess complicated features. In essence, the Monte Carlo Model is particularly useful for evaluating any option that cannot be estimated using a more straightforward formula, such as a Black-Scholes or Lattice based computation. As a result of this characteristic, the Monte Carlo Model is widely used in valuing path dependent options, such as lookbacks or real option analysis.