Application of Fuzzy Theory to Binomial Option Pricing Model
This paper presents an extension of the binomial option pricing model, which has the capabilities to cope with uncertain assumptions. Such assumptions are represented and dealt with in the framework of fuzzy theory. As the stock price can not be known exactly in advance, the approach of taking stock price as fuzzy price is more realistic and be easily accepted. In this paper, we take stock price in each node as fuzzy variable instead of crisp, then build a fuzzy binomial tree model and get numerical result in one period case. The simulation for fuzzy multiperiod binomial pricing model is also provided.
KeywordsOptions Binomial option pricing Fuzzy theory
Unable to display preview. Download preview PDF.
- 1.Appadoo, S., Thulasiram, R., Bector, C.: Fuzzy algebraic option pricing technique-A fundamental investigation. In: Proceeding on Administrative Sciences of Canada (ASAC), pp. 1–11 (2004)Google Scholar
- 2.Appadoo, S., Thulasiram, R., Bector, C.: CAPM assisted fuzzy binomial lattice method for option pricing. In: International Conference on Business and Finance, pp. 78–94 (2004)Google Scholar
- 3.Appadoo, S., Bector, C.: Binomial option pricing using O(2,2)trapezoidal type fuzzy numbers. In: Proceeding on Administrative Sciences of Canada (ASAC), pp. 46–58 (2005)Google Scholar
- 6.Han, L., Zheng, C.: Fuzzy options with application to default risk analysis for municipal bonds in China. In: World Congress of Nonlinear Analysis, pp. 2353–2365 (2005)Google Scholar
- 7.Han, L., Zheng, C.: Non-identical rationality in option pricing and fuzzy measures. Fuzzy Systems and Mathematics 16, 325–329 (2002) (in chinese)Google Scholar
- 10.Kaino, T., Hirota, K.: Differentiation of nonnegative measurable function choquet integral over real fuzzy measure space and its application to financial option trading model. In: Proc. of IEEE International Conference on Systems, Man, and Cybernetics, vol. 3, pp. 73–78 (1999)Google Scholar
- 15.Muzzioli, S., Reynaerts, H.: American option pricing with imprecise risk-neutral probabilities. International Journal of Approximate Reasoning 10, 1–8 (2007)Google Scholar