Fuzzy option value with stochastic volatility models

Uncertainty and vagueness play a central role in nan- cial models and fuzzy numbers can be a protable way to manage them. In this paper we generalize the Black and Scholes option valuation model (with constant volatility) to the framework of a volatility supposed to vary in a stochas- tic way. The models we take under consideration belongs to the main classes of stochastic volatility models: the endoge- nous and the exogenous source of risk. Fuzzy calculus for nancial applications requires massive computations and when a good parametric representation for fuzzy numbers is adopted, then the arithmetic operations and fuzzy calcu- lus can be efciently managed. Good in this context means that the shape of the resulting fuzzy numbers can be observed and studied in order to state fundamental properties of the model

Pricing Brazilian Exchange Rate Options Using An Adaptive Network-based Fuzzy Inference System

Recently, option pricing has become the focus of risk managers, policymakers, traders and more generally all market participants, since they find valuable information in these contracts. This paper suggests the pricing performance evaluation on Brazilian exchange rate R$(Reais) per US$ (U.S. Dollar) option contracts, traded at the Brazilian derivatives market, using an adaptive networkbased fuzzy inference system, for the period from April 1999 to April 2009. A fuzzy rule-based system was built with a family of conditional if-then statements whose consequent are functions of the antecedents, and then composed with the aid of fuzzy neurons. The ANFIS model was compared against the Black closedform formula and some neural networks topologies, considering traditional error measures and statistical tests. 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