Corporate and Project Finance Modeling: Theory and Practice (Wiley Finance) by Edward Bodmer

Author:Edward Bodmer
Language: eng
Format: mobi, epub
ISBN: 9781118854365
Publisher: Wiley
Published: 2014-10-10T04:00:00+00:00

Use of the continuous distribution prevents the possibility of a negative price (the EXP function cannot result in a negative value even when the volatility is negative) and involves mathematical equations that are a bit more complicated. If the time increments are continuous rather than discrete, the random walk becomes Brownian motion. In Brownian motion the term is a draw from a normal distribution with a variance that increases on a linear basis over time. If the variance is expressed on an annual basis, the variance for two years is twice the variance for one year. If the standard deviation or volatility is used rather than the variance, the increase for two years is multiplied by the square root of 2.

Figure 21.2 illustrates how you can add volatility into your model using the idea that the standard deviation should be adjusted by the square root of the time period in a year. The top part of Figure 21.2 demonstrates how to convert annual volatility into periodic volatility when your model is not an annual model. The lower part of Figure 21.2 demonstrates equations for applying the volatility, random variable, and normal distribution into your model. The base value before the time series is shown followed by the volatility and the random factor. Then the adjusted parameter is shown along with switch variables that allow you to turn the random process on and off.

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