| Binary options, the so-called digital options or two-valued options, is a kind of simplified financial instrument. Its operating simplicity makes binary options become one of the most popular varieties of financial transactions and the high-yield and high-risk characteristics determines the importance of its pricing. The traditional option pricing methods assume that the underlying asset price is determined when the option expires and do not take into account the uncertainty of the price. Fuzzy theory solved this problem. Fuzzy theory is a discipline to study the uncertainty of things. The combination of fuzzy theory and option pricing theory not only adapt to the market, but also make the market risk reduced, which promote the development of option pricing theory.In this paper, we study the binary option pricing problems based on the fuzzy theory, combine the traditional option pricing model theory with fuzzy theory, put forward a "deblurring" method, establish four binary options pricing models and give a numerical calculation to prove the convergence and effectiveness of the previous two models.Including the following:In chapter one, we describe the definition and characteristics of options and binary options and present the introduction, literature review, paper structure and innovation.In chapter two, detailed proof of the theorem about the probability and financial mathematic theory are presented and we give a brief introduction of the fuzzy theory.In chapter three, we propose a new binary option pricing method and construct four fuzzy asset option pricing models which based on the traditional option pricing models under the reasonable assumptions. In numerical simulation, select the 2012 daily settlement prices of the Cu1212 from the SHFE and obtain the price range of asset option with the support of MATLAB, which verify the convergence and effectiv-eness of the previous two models.In chapter four, we make a summary of the text and give an outlook. |
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