On theoretical pricing of options with fuzzy estimators

AbstractIn this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function, using statistical data. This application belongs to the financial field and especially to the section of financial engineering. In financial markets there are great fluctuations, thus the element of vagueness and uncertainty is frequent. This application concerns Theoretical Pricing of Options and in particular the Black and Scholes Options Pricing formula. We make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number. Furthermore we apply the Black and Scholes formula by using adaptive fuzzy numbers introduced by Thiagarajah et al. [K. Thiagarajah, S.S. Appadoo, A. Thavaneswaran, Option valuation model with adaptive fuzzy numbers, Computers and Mathematics with Applications 53 (2007) 831–841] for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value. We refer to both cases of call and put option prices according to the Black & Scholes model and also analyze the results to Greek parameters. Finally, a numerical example is presented for both methods and a comparison is realized based on the results

Low rank surrogates for polymorphic fields with application to fuzzy-stochastic partial differential equations

We consider a general form of fuzzy-stochastic PDEs depending on the interaction of probabilistic and non-probabilistic ("possibilistic") influences. Such a combined modelling of aleatoric and epistemic uncertainties for instance can be applied beneficially in an engineering context for real-world applications, where probabilistic modelling and expert knowledge has to be accounted for. We examine existence and well-definedness of polymorphic PDEs in appropriate function spaces. The fuzzy-stochastic dependence is described in a high-dimensional parameter space, thus easily leading to an exponential complexity in practical computations. To aleviate this severe obstacle in practise, a compressed low-rank approximation of the problem formulation and the solution is derived. This is based on the Hierarchical Tucker format which is constructed with solution samples by a non-intrusive tensor reconstruction algorithm. The performance of the proposed model order reduction approach is demonstrated with two examples. One of these is the ubiquitous groundwater flow model with Karhunen-Loeve coefficient field which is generalized by a fuzzy correlation length

The evaluation performance for commercial banks by intuitionistic fuzzy numbers: the case of Spain

In a globalized world, the banking sector has been forced to advance not only in financial performance, but also in non-financial performance, especially in sustainability criteria. For this purpose, multicriteria decision methods are especially suited to evaluate efficiency and to make a stable ranking of the most outstanding banks in the Spanish financial system. However, we are aware of the difficulties involved due to the inherent uncertainty and subjectivity of this process. For this reason, the use of fuzzy models is proposed, especially intuitionistic fuzzy numbers combined with the Analytic Hierarchy Process and the TOPSIS. The combination of financial criteria based on the CAMELS rating system with non-financial sustainability criteria makes it possible to order the Spanish banking system based on global efficiency. The most relevant contributions are: first, the use of intuitionistic fuzzy numbers in the performance evaluation process, whereby the quality of the information available can be quantified; and the most important one, a simplification of the process in the implementation of the intuitionistic fuzzy TOPSIS. Finally, through a sensibility analysis, it is possible to isolate the relevance of the sustainability process to obtain the global performance evaluation

Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions

[[abstract]]In the finance market, a short-term investment strategy is usually applied in portfolio selection in order to reduce investment risk; however, the economy is uncertain and the investment period is short. Further, an investor has incomplete information for selecting a portfolio with crisp proportions for each chosen security. In this paper we present a new method of constructing fuzzy portfolio model for the parameters of fuzzy-input return rates and fuzzy-output proportions, based on possibilistic mean–standard deviation models. Furthermore, we consider both excess or shortage of investment in different economic periods by using fuzzy constraint for the sum of the fuzzy proportions, and we also refer to risks of securities investment and vagueness of incomplete information during the period of depression economics for the portfolio selection. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model and a sensitivity analysis is realised based on the results.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙