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研究生： 楊啓斌
Yang, Chi-Pin
論文名稱： S&P 500指數價格密度函數及信念歧異
State Price density of S&P 500 index and heterogeneous beliefs
指導教授： 曾祺峰
Tzeng, Chi-Feng
口試委員: 楊睿中
Yang, Jui-Chung
冼芻蕘
Sin, Chor-yiu
學位類別： 碩士
Master
系所名稱： 科技管理學院 - 計量財務金融學系
Department of Quantitative Finance
論文出版年： 2018
畢業學年度： 106
語文別： 英文
論文頁數： 35
中文關鍵詞： 價格密度函數 、選擇權市場 、無風險偏態係數 、信念歧異
外文關鍵詞： state price density, Options markets, Risk-neutral skewness, heterogeneous beliefs
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    • 我們在此篇論文從隨機波動跳躍模型來估計出無風險密度函數 (risk-neutral density)的參數，以及利用GJR模型來模擬實際密度函數(real-world density)。接著利用這兩個函數就可以進一步獲得S&P 500指數的價格密度函數(SPD)，我們同時也測試SPD的斜率是否符合風險趨避假設。我們接著分別探討選擇權、股票、期貨市場的因素來解釋SPD的斜率，這些因素包含了價外的Put/Call的未平倉比率、價外Put 及Call的交易量、VIX指數、消費者情緒指數、投資人情緒指數、期貨交易量。這些因素都是和投資人對於市場的不同信念，我們要檢驗這些信念歧異是否確實會影響到價格密度函數。

    We first estimate the parameter of risk-neutral density from stochastic volatility jump (SVJ) model and those of GJR model to simulate real-world density. We can therefore obtain the state price density (SPD) of S&P500 from the two densities and test the risk aversion assumption that connected to the slope of SPD. We then investigate the factors from options, equity, and futures markets to explain the slope of SPD. The factors include the open interest ratio of the OTM put to call, the OTM call and put trading volume, CBOE’s VIX index, consumer sentiment index, investors sentiments index, and the volume of futures. These factors are all connected with different investor beliefs. Whether heterogeneous beliefs influence the state price density is tested.

    Contents I. Introduction.......................................... 1 II. Literature Review..................................... 3 III. Methodology........................................... 5 3.1 State Price Density (SPD)................................. 5 3.2 Stochastic Volatility (SV) model.......................... 6 3.3 Stochastic Volatility Jump (SVJ) model.................... 6 3.4 Risk Neutral Density (RND)................................ 7 3.5 Parametric Estimation..................................... 8 3.6 Glosten, Jagannathan & Runkle (GJR) model................. 8 3.7 Smoothing denisty to Real-World Density................... 9 3.8 Regression between S&P 500 SPD and heterogeneous beliefs.. 10 IV. Data.................................................. 11 V. Empirical Results..................................... 13 5.1 The Shape of S&P 500 SPDs................................. 13 5.1 Summary Statistics and Correlation Matric................. 17 5.3 Heterogeneous Beliefs to Investors........................ 27 VI. Conclusion............................................ 30 VII. References............................................... 31 VIII. Appendix................................................ 35 List of Figures Figure 1 State Price Density.................................. 14 Figure 2 Measure of Risk-Neutral Skewness and Heterogeneous Belief .............................................................. 21 List of Tables Table 1 Descriptive Statistics of Variables................... 18 Table 2 Options Data by Moneyness (K/S)....................... 22 Table 3 Options Data by Maturity.............................. 24 Table 4 Correlation Between Regression Variables.............. 26 Table 5 Heterogeneous Beliefs Results......................... 29

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