Application of fuzzy numbers in binomial tree model and time complexity
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Date
2013-08
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Technická Univerzita v Liberci
Technical university of Liberec, Czech Republic
Technical university of Liberec, Czech Republic
Abstract
Discrete binomial models are powerful tools for options valuation. For simple pay-off options they can be viewed as an approximation of famous Black-Scholes option valuation formula. By increasing the quantity of periods in binomial model (i.e. decreasing the length of the period), the results converge to the continuous model. However this approximation is very computationally costly, thus the analytical solution to the valuation is preferable. Nevertheless, the analytical solution does not exist for more complicated pay-off options. In the article we assume the valuation of project with the possibility to change the quantity of products produced. Some input parameters (concretely the volatility and initial cash-flows) are assumed to be uncertain and stated as a fuzzy numbers. Illustrative example is provided in the paper. In this example we examine the time complexity of the algorithm and the influence of the imprecision of input parameters on the appraisal imprecision. From the results it is apparent that the complexity of the model is quadratic. Thus by increasing the quantity of periods in the binomial model it becomes unreasonably time demanding.
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Subject(s)
finance, valuation, investment analysis, fuzzy sets, real options, binomial model
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978-80-7372-953-0