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Abstract Option market as a essential part of capital market, has the function of price finding, hedging and risk management, etc. There are plenty research focus on option pricing, volatility and hedging, but the research on market microstructure, especially on option bid-ask spread per se is sparse. This paper mainly focus on the effect of jump risk on option bid-ask spread. There are maturity effect of option bid-ask spread in each contract term, in order to remove the effect of maturity, we apply two method to detrend data: time to maturity method and functional data analysis method. After we remove the maturity effect, we confirm the effect of jump risk on option bid-ask spread. Based on the high-frequency data, we target on 27 stocks and options of S&P 500. Firstly realized jump variance is calculated using nonparametric method. Secondly maturity effect is removed using time to maturity method and functional data analysis method, respectively. At last we explore the effect of jump risk on option bid-ask spread using panel data regression. In our empirical analysis, we found that jump, does affect option bid-ask spread. Under time to maturity method, our regression shows that for one percent increase in jump density, the detrended option bid-ask spread will increase by 0.0075 percent, for for one percent increase in jump standard deviation, the intercept of detrended option bid-ask spread increase by 70.86% percent. Under functional data analysis method, our regression shows that for one percent increase in jump size mean, the detrended option bid-ask spread will decrease by 0.28 percent, taking jump factor as a whole, for one percent increase in jump, the detrended option bid-ask spread will decrease by 55.14 percent. Therefore, this paper empirically shows that jump has influence on option bidask spread. The Shanghai 50 ETF option is a symbol of the beginning of option era in China, our research also has empirical influence on China s option market. Key Words: Bid-ask spread, Jump, Functional data, III

8 ¹ Á... I Abstract... III 1 Ù XØ... 1 1.1 ïäµ Â....................................................... 1 1.2 ïäg µe....................................................... 2 1Ù znã... 5 2.1 ÏA.............................................................. 5 2.1.1 Ï½ þïñd............................................ 5 2.1.2 Ï½ þïa............................................ 7 2.2 ¼ê.êâ Û....................................................... 10 2.2.1 ¼ê.êâ Û {{....................................... 11 2.2.2 ¼ê.êâ²w?n {......................................... 11 2.3 yaåäç..................................................... 14 2.3.1 yaåäçïäuð.................................... 14 2.3.2 uÿa {................................................... 15 1nÙ.ï... 17 3.1 BSMÛ¹ÅÄÇ....................................................... 17 V

3.2 žmª³[ü......................................................... 18 3.3 ¼ê.êâ Û................................................... 20 3.3.1 ^¼ê.êâ Û?1²w?n................................ 20 3.3.2 ò v^l«ü........................................ 22 3.4 yaåäç..................................................... 24 3.5 êâ 8...................................................... 25 1oÙ y Û... 29 4.1 êâ................................................................... 29 4.2 (J`².............................................................. 33 4.2.1 [Üí'..................................................... 33 4.2.2 Ïžm{[Üí 8 Û.................................... 34 4.2.3 ¼ê.êâ Û{[Üí 8 Û............................. 37 4.2.4 \\N Cþ 8u......................................... 40 1ÊÙ (Ø... 43 5.1 Ì (Ø.............................................................. 43 5.2 Øv Ð"............................................................ 44 ë z... 47... 50 VI

Table of Contents Abstract in Chinese... I Abstract in English... III Chapter 1 Introduction... 1 1.1 Motivation and Background........................................... 1 1.2 Methodology and Structure............................................ 2 Chapter 2 Literature Review... 5 2.1 Maturity Effect........................................................ 5 2.1.1 Option Bid-Ask Spread............................................. 5 2.1.2 Maturity Effect in Option Market................................... 7 2.2 Functional Data Analysis.............................................. 10 2.2.1 History of Functional Data Analysis................................. 11 2.2.2 Smoothing the Functional Data..................................... 11 2.3 Realized Jump Variance............................................... 14 2.3.1 Development of Realized Jump Variance............................ 14 2.3.2 Detect the Jump.................................................... 15 Chapter 3 Model Setup... 17 3.1 BSM Implied Volatility................................................. 17 VII

3.2 Time to Maturity Method.............................................. 18 3.3 Functional Data Analysis Method...................................... 20 3.3.1 Smoothing Using Functional Data Analysis.......................... 20 3.3.2 Penalized Splines as Mixed Model.................................. 22 3.4 Realized Jump Variance............................................... 24 3.5 Panel Data Regression................................................. 25 Chapter 4 Empirical Analysis... 29 4.1 Data................................................................... 29 4.2 Result Analysis........................................................ 33 4.2.1 Comparison of Fitting Error......................................... 33 4.2.2 Fitting Error Regression Analysis of Time to Maturity Method........ 34 4.2.3 Fitting Error Regression Analysis of Functional Data Analysis Method............................................................ 37 4.2.4 Regression Test for Addition Variable............................... 40 Chapter 5 Conclusion... 43 5.1 Conclusion............................................................. 43 5.2 Problems and Future Work............................................ 44 Reference... 47 Acknowledgements... 50 VIII

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