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

Cheng Lee (), Gwo-Hshiung Tzeng () and Shin-Yun Wang ()

Review of Quantitative Finance and Accounting, 2005, vol. 25, issue 3, 255-275

Abstract: This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model. Copyright Springer Science + Business Media, Inc. 2005

Keywords: fuzzy set theory; fuzzy binomial OPM; option pricing model (OPM); a generalized CRR model; triangular fuzzy number; portfolio strategy (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s11156-005-4767-1

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