@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 Benemerita Universidad Autonoma 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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@RISK allowed us to measure derivative
prices by simulating random outcomes in
order to obtain a fair price for these
Dr. José Raul Castro Esparza
Benemerita Universidad Autonoma de Puebla
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Excerpted from Energy Risk Modeling, by Roy Nersesian, published by Palisade Corp.
This example uses @RISK to examine the nature of the loss function emanating from infrequent breakdowns or failures of critical components in a highly complex and capital intensive oil field production facility. From this an insurance premium will be devised for a self-insurance program to cover improbable occurrences of events that can be very costly in terms of loss of revenue. The derivation of the insurance premium will also allow the determination of minimum reserves in order for the self-insurance program to remain solvent.
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Interpreting AIC Statistics
The Akaike information criterion (AIC) is a measure of the relative quality of a statistical model for a given set of data. AIC deals with the trade-off between the goodness of fit of the model and the complexity of the model.
Q: @RISK gives me several candidate distributions. How can I interpret the AIC statistics? How much of a difference in AIC is significant?
The answer uses the idea of evidence ratios, derived from David R. Anderson's Model Based Inference in the Life Sciences: A Primer on Evidence (Springer, 2008), pages 89-91. The idea is that each fit has a delta, which is the difference between its AICc and the lowest of all the AICc values. (@RISK actually displays AICc, though the column heading is AIC; see the Palisade Knowledge base entry "Discrepancy in AIC Calculation?")
Example: Suppose that the normal fit has the lowest AICc, AICc = –110, and a triangular fit has AICc = –106. Then the delta for the triangular fit is (–106) – (–110) = 4.)
The delta for a proposed fit can be converted to an evidence ratio. Anderson gives a table, which can also be found on the Web. One place is page 26 of Burnham, Anderson, Huyvaert's "AIC model selection and multimodel inference in behavioral ecology", Behav Ecol Sociobiol (2011) 65:23–35 (PDF, accessed 2014-07-11). In the table, a delta of 4 corresponds to an evidence ratio of 7.4, meaning that the normal fit is 7.4 times as likely as the triangular fit to be the right fit. If you had to choose between those two only, there's a 7.4/8.4 = 88% chance that the normal is right, and a 1/8.4 = 12% chance that the triangular is right. But of course you usually have more than two fits to choose from.
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Economic Returns and Risk Analysis of Forage Wrapping
J. Ross Pruitt, Louisiana State University Agricultural Center;
R. Curt Lacy, University of Georgia; Dennis W. Hancock, University of Georgia
Use of bale wrapping technology allows beef cow-calf producers to lower their forage costs while improving the nutritional content of stored forages. Using stochastic simulation in @RISK, the authors evaluate the cost savings a cow-calf operation may experience by adopting this technology. This technology can lower per head feed costs for larger herds.
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