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August 11, 2024
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August 24, 2024
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Abstract

An option is a financial instrument that investors often use for speculation or hedging purposes. Calculating the profit in the investment using options also considers its price, so the investor needs to know the proper value of the option's price or at least the range of these values. This paper aims to improve the Bino-Trinomial tree model for determining the price of a European call option with a volatility parameter in the form of a triangular Fuzzy number. The Bino-Trinomial tree model is a combination of the Binomial and Trinomial trees that aims to control the values of its branches. Due to the involvement of the Fuzzy number, the obtained value of the option price is in a range or interval, so the investor could use it appropriately in arranging investment strategies. In the proposed model, the Fuzzy volatility parameter is utilized to capture the uncertainty of the estimated volatility in the financial market which can fluctuate from time to time. This parameter is expected to provide reasonable ranges and appropriate Fuzzy membership functions for option pricing so that investors can expect different optimal values for different risk preferences. We also adjusted the formulation of the increase and decrease factors in the Fuzzy Binomial tree to model stock price movements. Using different values of the volatility's sensitivity level and the option period, the results of numerical simulations show that prices of European call options given by the market are always within the option price range of the proposed model's result. Likewise, the results of the defuzzification of options prices in our Fuzzy Bino-Trinomial tree model are not much different from the prices given by the market. This shows that the Fuzzy Bino-Trinomial tree model performs better in determining the price of European call options than the Fuzzy Binomial tree and Fuzzy Trinomial models.

Keywords

Fuzzy volatility option pricing Bino-Trinomial tree model Binomial tree model Trinomial tree model

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Author Biographies

Novriana Sumarti, Institut Teknologi Bandung

Profesor in Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung 

Kuntjoro Adji Sidarto, Institut Teknologi Bandung

Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung

How to Cite
Agustina, F., Sumarti, N., & Sidarto, . K. A. (2024). CONSTRUCTION OF THE BINO-TRINOMIAL METHOD USING THE FUZZY SET APPROACH FOR OPTION PRICING. Journal of the Indonesian Mathematical Society, 30(2), 179–204. https://doi.org/10.22342/jims.30.2.1775.179-204
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