A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&amp;P 500 Index Options

Lee, Cheng Few; Tzeng, Gwo‐Hshiung; Wang, Shin-Yun

doi:10.1007/s11156-005-4767-1

Cited by 32 publications

(11 citation statements)

References 24 publications

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“…A subsequent paper [1] uses the Muzzioli and Torricelli model [49] to price an option with a fuzzy payoff when the up and down jump factors are represented by trapezoidal fuzzy numbers. Reference [29] proposes a fuzzy binomial (Cox-RossRubinstein [14]) option pricing model where both the interest rate ( r ) and the volatility parameter (σ ) are not crisp. In particular, rather than using triangular fuzzy numbers and fuzzy arithmetic, it supposes three scenarios for the up and down jump factors: low, medium and high volatility (which can be considered as the lower bound, the most possible value and the upper bound of the fuzzy number).…”

Section: Fuzzy Option Pricing Models In Discrete Timementioning

confidence: 99%

Fuzzy Approaches to Option Price Modeling

Muzzioli

Baets

2017

IEEE Trans. Fuzzy Syst.

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The aim of this paper is to review the literature that has addressed direct and inverse problems in option pricing in a fuzzy setting. In a direct problem, the stochastic process for the underlying asset is assumed and the option prices are derived by no-arbitrage or equilibrium conditions. In an inverse problem, the option prices are taken as given and used to infer the underlying asset process. Models are divided into discrete-time and continuous-time ones. Special attention is paid to real options, a particular class of non-financial options that are used to evaluate real investments. Directions for future research are outlined. In particular in inverse problems, there is still room for promising research, both in discrete time and in continuous time. Moreover, given that many proposed methods remain difficult to use in practice, there is mainly the need to apply the fuzzy models obtained on real market data and to compare the results with non-fuzzy techniques in order to assess the usefulness and the improvements in the modeling of imprecise data with fuzzy sets and fuzzy random variables.Index Terms-Finance, fuzzy binomial tree, fuzzy regression methods, fuzzy statistics and data analysis, inverse problems, volatility.

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Section: Fuzzy Option Pricing Models In Discrete Timementioning

confidence: 99%

Fuzzy Approaches to Option Price Modeling

Muzzioli

Baets

2017

IEEE Trans. Fuzzy Syst.

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“…In 2003, Carlsson and Fuller set up a real option pricing model for the fuzzy environment. Most of later scholars, along this way of thinking, improved fuzzy real option pricing models and their applications [33][34][35].…”

Section: Fuzzy Real Optionmentioning

confidence: 99%

Brownfield Redevelopment Evaluation Based on Fuzzy Real Options

2016

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There are a great amount of brownfield in Chinese mining cities. In order to promote mining cities sustainable development, it is necessary to redevelop brownfield. There is a great deal of uncertainty in the process of brownfield redevelopment owing to the influences of pollution. Normal fuzzy numbers were used to describe the fuzziness of the expected DCF (discounted cash flow) value of brownfield redevelopment projects. In view of experts' preferences, the weight of fuzzed estimation intervals of the expected DCF value was determined by means of the lattice closeness degree to find the volatility of the expected DCF value. Combining the results with the B-S (Black-Scholes) real option model, we built a fuzzy real option model which could be applied to the brownfield redevelopment projects. The empirical results showed that the valuation results of the fuzzy real option model, considering the experts' risk preferences, were relatively objective and accurate.

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“…19 An event is an experimental outcome that may or may not occur. The probability of a fuzzy event is used to measure the chance, the degree of compatibility, or degree of truth.…”

Section: Probability Of Fuzzy Eventsmentioning

confidence: 99%

A Fuzzy Real Option Valuation Approach to Capital Budgeting Under Uncertainty Environment

Wang

Lee

2010

Int. J. Info. Tech. Dec. Mak.

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The information needed for capital budgeting is generally not known with certainty. The sources of uncertainty may be the net cash inflows, the life of the project, or the discount rate. We propose a capital budgeting model under uncertainty environment in which the concept of probability is employed in describing fuzzy events and cash flow information can be specified as a special type of fuzzy numbers. The present worth of each fuzzy project cash flow can be subsequently estimated. At the same time, to select fuzzy projects and determine the optimal decision time under limited capital budget, we offer an example to analyze the results of the capital budgeting problem under uncertainty using a fuzzy real option valuation.

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A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&P 500 Index Options

Cited by 32 publications

References 24 publications

Fuzzy Approaches to Option Price Modeling

Fuzzy Approaches to Option Price Modeling

Brownfield Redevelopment Evaluation Based on Fuzzy Real Options

A Fuzzy Real Option Valuation Approach to Capital Budgeting Under Uncertainty Environment

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