臺灣博碩士論文加值系統

Option is a tool that investors often use to arbitrage or hedge. However, either Black-Scholes model or CRR model can only provide a theoretical reference value. This paper applies fuzzy set to the CRR model. It is expected that the fuzzy volatility, instead of the crisp one as in conventional CRR model, can provide reasonable ranges and corresponding memberships of option prices. As a result, investors with various risk preferences can interpret the optimal differently.

Contents

1.Introduction•••••••••••••••••••••••1
2. Literature Review•••••••••••••••••••••2
3. Research Methods•••••••••••••••••••••3
3.1 Fuzzy Theory••••••••••••••••••••••3
3.1.1 Triangular Fuzzy Number••••••••••••••••3
3.1.2 Fuzzy Relation•••••••••••••••••••••3
3.2 Option Pricing Model•••••••••••••••••••4
3.3 The Types of Volatility••••••••••••••••••5
4. Fuzzy Binomial Tree Option Pricing Model•••••••••••9
4.1 One-Step Fuzzy Period Pricing Model••••••••••••9
4.2 Inference of Fuzzy Binomial Tree Option Pricing Model•••••11
4.3 Two-Step Fuzzy Pricing Model•••••••••••••••13
4.4 N-Step Fuzzy Pricing Model •••••••••••••••14
5. Experimental Analysis ••••••••••••••••••28
5.1 Data Description and Characteristics•••••••••••••28
5.2 The Fuzzy Tree of Stock Price•••••••••••••••29
5.3 The Fuzzy Tree of Option Price ••••••••••••••32
5.4 Sensitivity Analysis•••••••••••••••••••34
6. Conclusions ••••••••••••••••••••••35
6.1 Summary •••••••••••••••••••••••35
6.2 Future work ••••••••••••••••••••••36

References••••••••••••••••••••••37

References
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