@RISK Improves Upon Black-Scholes Options Pricing Method


The financial world holds a great deal of risk. To help balance some of the unknowns, Dr. José Raúl Castro Esparza, professor at Benemérita Universidad Autónoma de  Puebla, in Puebla, Mexico has used @RISK to create a more exact and accurate pricing strategy for a key financial tool, the derivative. He has used this model as a teaching tool for both graduate and undergraduate students in the Actuarial Sciences and Masters of Finance programs at his university.

Derivatives are, in essence, a security whose price depends on the performance of one or more underlying assets. Companies often buy derivatives to help manage risk, as these tools can be viewed as a form of insurance policy. But how does the seller of the derivative determine its price?

The typical technique used is known as the Black-Scholes method, which takes into account the current price of the asset, the average price of the asset during the past, and how many days, months, or years into the future the asset will be bought (i.e. time until expiration of the option). Additionally, the formula incorporates a “white noise” element—which stands in as the inherent uncertainty that cannot be measured.

However, the Black-Scholes method doesn’t fully capture reality. “Real life doesn’t statistically behave in those normal distributions,” says Dr. Castro.  As an alternative, he applied a Monte Carlo method, based on the “Random Walk Model” (a mathematical formalization of random movement) that uses the appropriate statistical distribution to model random errors, and designed an interactive model in Excel VBA so that users could easily access this tool for pricing options.

@RISK’s customizability and ease-of-use made his option pricing program possible, says Dr. Castro. “I was able to develop this capability with Palisade’s software, creating a much more accurate and simple method of determining the price of these derivatives.”

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