A new application of fuzzy set theory to the Black-Scholes option pricing model

Authors:
Cheng-Few Lee;Gwo-Hshiung Tzeng;Shin-Yun Wang
Affiliations:
Department of Finance, Rutgers University, New Brunswick, NJ, USA/ Institure of Finance, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 3000, Taiwan;Department of Business Administration, Kainan University, No. 1, Kai-Nan Rd., Luchu, Taoyuan 338, Taiwan/ Institute of Management of Technology, National Chiao Tung University, 1001 Ta-Hsueh Road, ...;Institute of Management of Technology, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300, Taiwan/ Department of Finance, National Dong Hwa University, 1, Sec. 2, Da-Hsueh Rd., Shou-F ...
Venue:
Expert Systems with Applications: An International Journal
Year:
2005

Citing 0
Cited 10

Fuzzy set theory in managerial contract analyses

Expert Systems with Applications: An International Journal
Recent Literature

Fuzzy Sets and Systems
Investment project valuation based on a fuzzy binomial approach

Information Sciences: an International Journal
Investment project valuation using a fuzzy real options approach

ISTASC'10 Proceedings of the 10th WSEAS international conference on Systems theory and scientific computation
Option price sensitivities through fuzzy numbers

Computers & Mathematics with Applications
Calibrating parametric exponential Lévy models to option market data by incorporating statistical moments priors

Expert Systems with Applications: An International Journal
Investment appraisal under uncertainty - a fuzzy real options approach

ICONIP'10 Proceedings of the 17th international conference on Neural information processing: models and applications - Volume Part II
A study of Greek letters of currency option under uncertainty environments

Mathematical and Computer Modelling: An International Journal
A fuzzy real option approach for investment project valuation

Expert Systems with Applications: An International Journal
Pricing and hedging in a single period market with random interval valued assets

International Journal of Approximate Reasoning

Quantified Score

Hi-index	12.06

Visualization

Abstract

The Black-Scholes Option pricing model (OPM) developed in 1973 has always been taken as the cornerstone of option pricing model. The generic applications of such a model are always restricted by its nature of not being suitable for fuzzy environment since the decision-making problems occurring in the area of option pricing are always with a feature of uncertainty. When an investor faces an option-pricing problem, the outcomes of the primary variables depend on the investor's estimation. It means that a person's deduction and thinking process uses a non-binary logic with fuzziness. Unfortunately, the traditional probabilistic B-S model does not consider fuzziness to deal with the aforementioned problems. The purpose of this study is to adopt the fuzzy decision theory and Bayes' rule as a base for measuring fuzziness in the practice of option analysis. This study also employs 'Fuzzy Decision Space' consisting of four dimensions, i.e. fuzzy state; fuzzy sample information, fuzzy action and evaluation function to describe the decision of investors, which is used to derive a fuzzy B-S OPM under fuzzy environment. Finally, this study finds that the over-estimation exists in the value of risk interest rate, the expected value of variation stock price, and in the value of the call price of in the money and at the money, but under-estimation exists in the value of the call price of out of the money without a consideration of the fuzziness. ey without a consideration of the fuzziness.