Option Pricing Model with Fuzzy Measures under Knightian Uncertainty |
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| Institution: | 1. Institute of Information Management, National Chiao-Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, ROC;2. Department of Information and Finance Management, Institute of Information Management and Finance, National Chiao-Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, ROC;3. Department of Finance and Department of Computer Science & Information Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, ROC;1. 277 Park Avenue, New York, NY-10172, United States;2. Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL-32306, United States |
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| Abstract: | Conventionally, the risk is described with a unique probability measure. However, Ellsberg paradox indicates that the existence of Knightian uncertainty would have an effect on both decision-makers' behavior and asset pricing. In this article, an option-pricing model is proposed under Knightian uncertainty using the λ-fuzzy measure and the Choquet integral, and the equilibrium price of European option on a non-dividend-paying stock is deduced. The equilibrium price is found to be an interval instead of a determinate number, which is in accordance with the conclusion of Epstein conclusion. Subsequent experimental research and the outcome indicate that the parameter λ which can describe human subjective sentimental will change with volatility of personal mood. Moreover, this study will pave a novel way to cope with other derivatives pricing under Knightian uncertainty. |
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