Financial Simulation Modeling in Excel

DIFFERENCES BETWEEN PROJECTING DEFAULTS AND PRICE MOVEMENTS

While there are many applications of Monte Carlo simulations, the two most frequently used are for measuring defaults and price movements. While equivalences can be drawn between values and defaults (such as in the Merton Model), we still need to account for the fact that default is a binary situation, whereas price can theoretically move to infinitely different levels. In order to account for this difference for Asset A in period i, we will start with the random draw variable R. In this construct, the movement of asset price (in a price simulation) will be produced as a function of the randomly drawn variable as in equation 6.1:

In this, we can see that the change in price of the asset is based on a percentage of the price in the previous period. The function f(R_i) is defined by mapping the randomly drawn number to a price movement. In many cases, a drift term, μ, will be added to this movement. However, for default simulations, we can use a number of methodologies. A very-in-depth simulation might use structural models for each asset, and as a result default is created by asset movements considering the capital structure of each company. However, for reduced form models, the forecasting is much simpler. We have a probability of default for each period D. We will simply draw a uniformly distributed random number R, and ...