Option pricing and the Greeks under Gaussian fuzzy environments

Abstract

This work considers pricing European call options and the study of Greek letters of options under a fuzzy environment. In the past work, stock prices are usually represented by symmetric triangular fuzzy numbers for the computational convenience while pricing options with uncertainty. It might not be enough to explain the stochastic nature of the underlining price in the option pricing formula. This work considers developing the fuzzy pattern of European call option under the assumption of the stock return being a Gaussian fuzzy number. The study of Greeks for the sensitivity analysis of the fuzzy call option price with respect to the change in the pricing variables is included. The empirical analysis and comparison on the fuzzy European option pricing based on the real market data of SPX options at CBOE are provided. Our results show that the fuzzy options are more close to the theoretical options derived from the Black–Scholes formula while employing Gaussian fuzzy stock returns for pricing European call options.

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Notes

  1. 1.

    https://stats.bis.org/statx/srs/table/d5.1.

  2. 2.

    https://www.theocc.com/webapps/historical-volume-query.

  3. 3.

    http://www.cboe.com/delayedquote/quote-table?ticker=SPX.

  4. 4.

    The data source on the February 16, 2018, rate. http://www.optionistics.com/quotes/stock-option-chains/SPX.

  5. 5.

    The data source on the February 16, 2018, rate. https://www.federalreserve.gov/releases/h15/.

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Correspondence to Hong-Ming Chen.

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Chen, H., Hu, C. & Yeh, W. Option pricing and the Greeks under Gaussian fuzzy environments. Soft Comput 23, 13351–13374 (2019). https://doi.org/10.1007/s00500-019-03876-w

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Keywords

  • Gaussian fuzzy number
  • Options
  • Greeks
  • SPX
  • Optimization