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

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  • Cheng Lee
  • Gwo-Hshiung Tzeng
  • Shin-Yun Wang

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

Suggested Citation

  • Cheng Lee & Gwo-Hshiung Tzeng & Shin-Yun Wang, 2005. "A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&P 500 Index Options," Review of Quantitative Finance and Accounting, Springer, vol. 25(3), pages 255-275, November.
    • Handle: RePEc:kap:rqfnac:v:25:y:2005:i:3:p:255-275
    DOI: 10.1007/s11156-005-4767-1
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    3. Smimou, K. & Bector, C.R. & Jacoby, G., 2008. "Portfolio selection subject to experts' judgments," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 1036-1054, December.
    4. Zmeskal, Zdenek, 2010. "Generalised soft binomial American real option pricing model (fuzzy-stochastic approach)," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1096-1103, December.
    5. In Kim & In-Seok Baek & Jaesun Noh & Sol Kim, 2007. "The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics," Review of Quantitative Finance and Accounting, Springer, vol. 29(1), pages 69-110, July.
    6. Marek Z. Reformat & Ronald R. Yager, 2015. "Soft Computing Techniques for Querying XBRL Data," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 22(3), pages 179-199, July.
    7. Yow-Jen Jou & Chih-Wei Wang & Wan-Chien Chiu, 2013. "Is the realized volatility good for option pricing during the recent financial crisis?," Review of Quantitative Finance and Accounting, Springer, vol. 40(1), pages 171-188, January.
    8. Ozge Yasar & Tulay Korkusuz Polat, 2022. "A Fuzzy-Based Application for Marketing 4.0 Brand Perception in the COVID-19 Process," Sustainability, MDPI, vol. 14(24), pages 1-22, December.

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