臺灣博碩士論文加值系統

本研究目的在於，在「delta避險」策略下，探討波動度風險是否評價入VXX選擇權市場。「delta避險」策略，是指持有長部位的選擇權，並同時以現貨避險直到到期日所構成的選擇權投資組合。研究對象為VXX選擇權，發行於芝加哥期權交易所(CBOE)，資料期間自2010年4月6日至2016年6月16日。本篇論文使用了3種波動，分別是GARCH波動和歷史波動，以及參照VIX指數的編制方法，編制VXX選擇權波動率指數。分析結果顯示，「delta避險」的VXX選擇權投資組合之風險溢酬為負的，且在特定波動下，檢定結果可證明存在波動風險溢酬。

The purpose of this study is to investigate whether volatility risk is priced in the VXX options market by constructing delta-hedged option portfolio (set the option long and hedge with stock). Data from the Chicago Board Options Exchange are used in this research, covering the period from April 6, 2010, to June 16, 2016. There are three kind of volatility measurements in this paper, including GARCH volatility, historical volatility, and volatility index calculated by the VIX methodology. Results show that the delta-hedged portfolio underperforms zero, which implies a negative risk premium. Under the specific volatility measurements, the evidence is supporting that a volatility risk premium exist in the VXX options market.

一、介紹與文獻回顧 1
二、研究方法 6
三、資料 9
四、分析結果 10
五、結論 14
六、參考文獻 15
七、附錄 20

[1] Arisoy, T.E., A. Salih, and L. Akdeniz (2007), “ Is volatility risk priced in the securities market? Evidence from S&P 500 index options,”Journal of Futures Markets, 27, 617-642.

[2] Bakshi, G. and N. Kapadia, (2003a), “Delta-hedged gains and the negative market volatility risk premium,”Review of Financial Studies, 16, 527-566.

[3] Bakshi, G., N. Kapadia, and D. Madan, 2003. Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options. Review of Financial Studies 16:101–43.

[4] Bansal, R. and I. Shaliastovich, 2010, Confidence Risk and Asset Prices, American Economic Review 100(2), 537–541.

[5] Bansal, R., D. Kiku, and A. Yaron, 2010, Long Run Risks, the Macroeconomy, and Asset Prices, American Economic Review 100(2), 542–546.

[6] Bao, Q., S. Li, and D. Gong, 2012, Pricing VXX option with default risk and positive volatility skew, European Journal of Operational Research 223, 246–255.

[7] Bates, D.S. (2000), “Post-87 crash fears in S&P 500 futures options,”Journal of Econometrics, 94, 181-238.

[8] Bollerslev, T., G. Tauchen, and H. Zhou, 2009. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22(11): 4463-4492.

[9] Bollerslev, T., M. Gibson, and H. Zhou, 2011, Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-Implied and Realized Volatilities, 52 Journal of Econometrics, 102–118.

[10] Bondarenko, O., 2004, Market price of variance risk and performance of hedge funds, Working paper, University of Illinois, Chicago.

[11] Carr, P. and L.Wu (2009),“Variance risk premiums,” Review of Financial Studies, 22, 1311–1342.

[12] Da, Z., and E. Schaumburg, 2011. The pricing of volatility risk across asset classes and the FamaFrench factors, Working paper, Northwestern University.

[13] Deng, G., C. McCann, and O. Wang, 2012, Are VIX Futures ETPs Effective Hedges?, The Journal of Index Investing 3, 35–48.

[14] Diavatopoulos, D., J. S. Doran, A. Fodor, and D. R. Peterson (2012). ‘The information content of implied skewness and kurtosis changes prior to earnings announcements for stock and option returns’, Journal of Banking and Finance, 36 (3), pp. 786-802.

[15] Duan, J. and C. Yeh, (2007), Jump and volatility risk premiums implied by VIX, Journal of Economic Dynamics and Control 34, 2232-2244.

[16] Feng, Y., J. Song, and C.-F. Wu, (2006), “Down-side risk and the puzzle of implied volatilitypremium,”Working Paper, Shanghai Jiao Tong University.

[17] Figlewski, S. (1994) ‘Forecasting volatility using historical data.’ New York University Working Paper S-94-13.

[18] Fouque, J.P., G. Papanicolaou, and K.R. Sircar, (2000). Derivatives in Financial Markets with Stochastic Volatility. Princeton University Press, Princeton

[19] Gehricke, S. (2015). Modeling VXX Price (Thesis, Master of Business). University of Otago. Retrieved from http://hdl.handle.net/10523/5502

[20] Goyal, A. (2000), “Predictability of Stock Return Volatility from GARCH Models”, Working Paper, Anderson Graduate School of Management, UCLA. May.

[21] Guo, D.,1998, “The Risk Premium of Volatility Implicit in Currency Options,” Journal of Business and Economic Statistics 16, 498-507.

[22] Hancock, G. 2013a. “Inverse VIX Futures ETNs: Caveat Emptor.” Journal of Index Investing 4:2, 23-33.

[23] Hancock, G. 2013b. “VIX Futures ETNs: Three Dimensional Losers.” Accounting and Finance Research 2:3, 53-64.

[24] Hao, J. and J. E. Zhang (2013): “GARCH Option Pricing Models, the CBOE VIX, and Variance Risk Premium,” Journal of Financial Econometrics, 11, 556–580.

[25] Husson, T. and C. McCann, 2011, The VXX ETN and Volatility Exposure, PIABA Bar Journal 18, 235–252.

[26] Jackwerth, J.C. and M. Rubinstein, 1996, Recovering probability distributions from option prices, Journal of Finance 51, 1611–1631.

[27] Low, B.S. and S. Zhang, 2005. The volatility risk premium embedded in currency options. Journal of Financial and Quantitative Analysis 40(4): 803–832.

[28] Melino, A. and S. Turnbull, 1995. Misspecification and the pricing and hedging of long-term foreign currency options. Journal of International Money and Finance 14, 373-393.

[29] Todorov, V., 2009, Variance Risk Premium Dynamics: The Role of Jumps, Review of Financial Studies, 23, 345-383.

[30] Whaley, R.E., 2013, Trading Volatility: At What Cost, The Journal of Portfolio Management 40, 95–108.

[31] Yan, G. and F.B. Hanson, Option pricing for a stochastic-volatility, jump-diffusion models, with log-uniform jump-amplitudes, Proceedings of the 2006 American Control Conference (2006), pp. 2989–2994.