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題名 基於隱含隨機波動度模型之最小變異 Delta 避險策略 —以外匯選擇權市場為例
Minimum-Variance Delta Hedging Strategy based on Implied Stochastic Volatility Model : An Empirical Study on the FX Options Market作者 林崇仁
Lin, Chung-Jen貢獻者 林士貴<br>羅秉政
Lin, Shih-Kuei<br>Kendro Vincent
林崇仁
Lin, Chung-Jen關鍵詞 外匯市場
隨機波動度模型
最小變異 Delta
避險
Forex
Stochastic Volatility Model
Minimum Variance Delta
Hedge日期 2023 上傳時間 2-Aug-2023 14:11:33 (UTC+8) 摘要 本研究以外匯市場中USD/JPY作為研究對象，在模型方面，採用Aït-Sahalia et al.(2021)提出的Implied Stochastic Volatility Model(ISVM)，透過提出新的估計方法來建構隱含波動度曲面，與Heston模型進行模型比較，探討兩模型於隱含波動度曲面上之樣本內配適情形。而在風險管理方面，透過Minimum Variance Delta避險策略，相對於一般常見的Delta避險策略，不同的地方在於其除了考慮在資產價格變動下投資組合的影響外，亦同時考慮資產價格變動對於隱含波動度之影響考慮資產價格變化對於隱含波動度之影響。由實證結果顯示，在模型配適上，ISVM模型配適結果優於Heston模型。而在避險績效上，使用MV Delta避險策略之避險效果優於一般Delta避險策略，其中又以ISVM 模型最佳。此外，透過拆分subsample探討在極端的金融環境下，亦可發現不論是Heston模型或是ISVM模型，在高波動時期相比於低波動之穩定時期之績效表現較佳。
This study focuses on the USD/JPY pair in the foreign exchange market. In terms of model construction, we adopt the Implied Stochastic Volatility Model (ISVM) as proposed by Aït-Sahalia et al. (2021). We compare this model to the Heston model to examine their respective fitness on the implied volatility surface. Empirical results indicate that the ISVM model outperform the Heston model.In terms of risk management, we adopt the Minimum Variance Delta hedging strategy, which distinguishes itself from conventional Delta hedging by consider- ing not only the influence of asset price changes on the portfolio but also the impact of these price changes on implied volatility. Our empirical results demonstrate that the hedging performance using the MV Delta strategy outperforms that of the conventional Delta hedging strategy, with the ISVM model performing optimally. Moreover, by splitting into subsamples to investigate under extreme financial conditions, we observe that both the Heston and ISVM models perform better during periods of high volatility as compared to periods of low and stable volatility.參考文獻 [1] Ahlip, R. and Rutkowski, M. (2013). Pricing of foreign exchange options under the heston stochastic volatility model and cir interest rates. Quantitative Finance, 13(6):955–966.[2] Aït-Sahalia, Y., Li, C., and Li, C. X. (2021). Implied stochastic volatility models. The Review of Financial Studies, 34(1):394–450.[3] Alexander, C. and Kaeck, A. (2012). Does model fit matter for hedging? evidence from ftse 100 options. Journal of Futures Markets, 32(7):609–638.[4] Alexander, C. and Nogueira, L. M. (2007). Model-free hedge ratios and scale-invariant models. Journal of Banking & Finance, 31(6):1839–1861.[5] Alexander, C., Rubinov, A., Kalepky, M., and Leontsinis, S. (2012). Regime-dependent smile- adjusted delta hedging. Journal of Futures Markets, 32(3):203–229.[6] Almeida, C., Fan, J., Freire, G., and Tang, F. (2022). Can a machine correct option pricing models? Journal of Business & Economic Statistics, pages 1–14.[7] Amin, K. I. and Jarrow, R. A. (1991). Pricing foreign currency options under stochastic interest rates. Journal of International Money and Finance, 10(3):310–329.[8] Andersen, L. and Andreasen, J. (2000). Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. Review of Derivatives Research, 4:231–262.[9] Bakshi, G., Cao, C., and Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of Finance, 52(5):2003–2049.[10] Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. The Review of Financial Studies, 9(1):69–107.[11] Bates, D. S. (2000). Post-’87 crash fears in the s&p 500 futures option market. Journal of Econometrics, 94(1-2):181–238.[12] Bates, D. S. (2012). Us stock market crash risk, 1926–2010. Journal of Financial Economics, 105(2):229–259.[13] Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1- 2):167–179.[14] Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637–654.[15] Bossens, F., Rayée, G., Skantzos, N. S., and Deelstra, G. (2010). Vanna-volga methods applied to fx derivatives: from theory to market practice. International Journal of Theoretical and Applied Finance, 13(08):1293–1324.[16] Branger, N., Krautheim, E., Schlag, C., and Seeger, N. (2012). Hedging under model misspecification: All risk factors are equal, but some are more equal than others.... Journal of Futures Markets, 32(5):397–430.[17] Carr, P. and Cousot, L. (2011). A pde approach to jump-diffusions. Quantitative Finance, 11(1):33–52.[18] Carr, P. and Cousot, L. (2012). Explicit constructions of martingales calibrated to given implied volatility smiles. SIAM Journal on Financial Mathematics, 3(1):182–214.[19] Carr, P., Geman, H., Madan 5, D. B., and Yor, M. (2004). From local volatility to local lévy models. Quantitative Finance, 4(5):581–588.[20] Cheng, H.-W., Chang, L.-H., Lo, C.-L., and Tsai, J. T. (2023). Empirical performance of component garch models in pricing vix term structure and vix futures. Journal of Empirical Finance, 72:122–142.[21] Christie, A. A. (1982). The stochastic behavior of common stock variances: Value, leverage and interest rate effects. Journal of Financial Economics, 10(4):407–432.[22] Christoffersen, P. and Jacobs, K. (2004). The importance of the loss function in option valuation. Journal of Financial Economics, 72(2):291–318.[23] Christoffersen, P., Jacobs, K., and Mimouni, K. (2010). Volatility dynamics for the s&p500: Evidence from realized volatility, daily returns, and option prices. The Review of Financial Studies, 23(8):3141–3189.[24] Christoffersen, P., Jacobs, K., and Ornthanalai, C. (2012). Dynamic jump intensities and risk premiums: Evidence from s&p500 returns and options. Journal of Financial Economics, 106(3):447–472.[25] Cont, R. and Da Fonseca, J. (2002). Dynamics of implied volatility surfaces. Quantitative Finance, 2(1):45.[26] Cox, J. C., Ingersoll Jr, J. E., and Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica: Journal of the Econometric Society, pages 363–384.[27] Duffie, D., Pan, J., and Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6):1343–1376.[28] Dumas, B., Fleming, J., and Whaley, R. E. (1998). Implied volatility functions: Empirical tests. The Journal of Finance, 53(6):2059–2106.[29] Dupire, B. et al. (1994). Pricing with a smile. Risk, 7(1):18–20.[30] Garman, M. B. and Kohlhagen, S. W. (1983). Foreign currency option values. Journal ofInternational Money and Finance, 2(3):231–237.[31] Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6(2):327–343.[32] Hull, J. and White, A. (1987). The pricing of options on assets with stochastic volatilities. The Journal of Finance, 42(2):281–300.[33] Hull, J. and White, A. (2017). Optimal delta hedging for options. Journal of Banking and Finance, 82:180–190.[34] Lee, R. W. (2001). Implied and local volatilities under stochastic volatility. International Journal of Theoretical and Applied Finance, 4(01):45–89.[35] Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, pages 141–183.[36] Nandi, S. (1996). Pricing and hedging index options under stochastic volatility: an empirical examination. Technical report, Working paper.[37] Ornthanalai, C. (2014). Levy jump risk: Evidence from options and returns. Journal of Financial Economics, 112(1):69–90. 描述 碩士
國立政治大學
金融學系
110352029資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110352029 資料類型 thesis dc.contributor.advisor 林士貴<br>羅秉政 zh_TW dc.contributor.advisor Lin, Shih-Kuei<br>Kendro Vincent en_US dc.contributor.author (Authors) 林崇仁 zh_TW dc.contributor.author (Authors) Lin, Chung-Jen en_US dc.creator (作者) 林崇仁 zh_TW dc.creator (作者) Lin, Chung-Jen en_US dc.date (日期) 2023 en_US dc.date.accessioned 2-Aug-2023 14:11:33 (UTC+8) - dc.date.available 2-Aug-2023 14:11:33 (UTC+8) - dc.date.issued (上傳時間) 2-Aug-2023 14:11:33 (UTC+8) - dc.identifier (Other Identifiers) G0110352029 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/146601 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融學系 zh_TW dc.description (描述) 110352029 zh_TW dc.description.abstract (摘要) 本研究以外匯市場中USD/JPY作為研究對象，在模型方面，採用Aït-Sahalia et al.(2021)提出的Implied Stochastic Volatility Model(ISVM)，透過提出新的估計方法來建構隱含波動度曲面，與Heston模型進行模型比較，探討兩模型於隱含波動度曲面上之樣本內配適情形。而在風險管理方面，透過Minimum Variance Delta避險策略，相對於一般常見的Delta避險策略，不同的地方在於其除了考慮在資產價格變動下投資組合的影響外，亦同時考慮資產價格變動對於隱含波動度之影響考慮資產價格變化對於隱含波動度之影響。由實證結果顯示，在模型配適上，ISVM模型配適結果優於Heston模型。而在避險績效上，使用MV Delta避險策略之避險效果優於一般Delta避險策略，其中又以ISVM 模型最佳。此外，透過拆分subsample探討在極端的金融環境下，亦可發現不論是Heston模型或是ISVM模型，在高波動時期相比於低波動之穩定時期之績效表現較佳。 zh_TW dc.description.abstract (摘要) This study focuses on the USD/JPY pair in the foreign exchange market. In terms of model construction, we adopt the Implied Stochastic Volatility Model (ISVM) as proposed by Aït-Sahalia et al. (2021). We compare this model to the Heston model to examine their respective fitness on the implied volatility surface. Empirical results indicate that the ISVM model outperform the Heston model.In terms of risk management, we adopt the Minimum Variance Delta hedging strategy, which distinguishes itself from conventional Delta hedging by consider- ing not only the influence of asset price changes on the portfolio but also the impact of these price changes on implied volatility. Our empirical results demonstrate that the hedging performance using the MV Delta strategy outperforms that of the conventional Delta hedging strategy, with the ISVM model performing optimally. Moreover, by splitting into subsamples to investigate under extreme financial conditions, we observe that both the Heston and ISVM models perform better during periods of high volatility as compared to periods of low and stable volatility. en_US dc.description.tableofcontents 目錄摘要 iAbstract iiContents iiiList of Figures vList of Tables vi第一章 緒論 1第一節 研究背景 1第二節 研究動機 2第三節 研究目的 5第二章 文獻回顧 7第一節 隨機波動度模型沿革 7第二節 外匯市場隨機波動度模型之研究 8第三節 最小變異Delta避險之研究 9第三章 研究方法 10第一節 Heston Model 10第二節 Implied Stochastic Volatility Model 13第三節 Minimum Variance Delta Hedging 17第四章 實證研究 21第一節 資料描述 21第二節 模型配適比較 23第三節 避險績效表現 25第五章 結論與未來展望 34第一節 結論 34第二節 未來展望 35參考文獻 36附錄 39 zh_TW dc.format.extent 2237585 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110352029 en_US dc.subject (關鍵詞) 外匯市場 zh_TW dc.subject (關鍵詞) 隨機波動度模型 zh_TW dc.subject (關鍵詞) 最小變異 Delta zh_TW dc.subject (關鍵詞) 避險 zh_TW dc.subject (關鍵詞) Forex en_US dc.subject (關鍵詞) Stochastic Volatility Model en_US dc.subject (關鍵詞) Minimum Variance Delta en_US dc.subject (關鍵詞) Hedge en_US dc.title (題名) 基於隱含隨機波動度模型之最小變異 Delta 避險策略 —以外匯選擇權市場為例 zh_TW dc.title (題名) Minimum-Variance Delta Hedging Strategy based on Implied Stochastic Volatility Model : An Empirical Study on the FX Options Market en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Ahlip, R. and Rutkowski, M. (2013). Pricing of foreign exchange options under the heston stochastic volatility model and cir interest rates. Quantitative Finance, 13(6):955–966.[2] Aït-Sahalia, Y., Li, C., and Li, C. X. (2021). Implied stochastic volatility models. The Review of Financial Studies, 34(1):394–450.[3] Alexander, C. and Kaeck, A. (2012). Does model fit matter for hedging? evidence from ftse 100 options. Journal of Futures Markets, 32(7):609–638.[4] Alexander, C. and Nogueira, L. M. (2007). Model-free hedge ratios and scale-invariant models. Journal of Banking & Finance, 31(6):1839–1861.[5] Alexander, C., Rubinov, A., Kalepky, M., and Leontsinis, S. (2012). Regime-dependent smile- adjusted delta hedging. Journal of Futures Markets, 32(3):203–229.[6] Almeida, C., Fan, J., Freire, G., and Tang, F. (2022). Can a machine correct option pricing models? Journal of Business & Economic Statistics, pages 1–14.[7] Amin, K. I. and Jarrow, R. A. (1991). Pricing foreign currency options under stochastic interest rates. Journal of International Money and Finance, 10(3):310–329.[8] Andersen, L. and Andreasen, J. (2000). Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. Review of Derivatives Research, 4:231–262.[9] Bakshi, G., Cao, C., and Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of Finance, 52(5):2003–2049.[10] Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. The Review of Financial Studies, 9(1):69–107.[11] Bates, D. S. (2000). Post-’87 crash fears in the s&p 500 futures option market. Journal of Econometrics, 94(1-2):181–238.[12] Bates, D. S. (2012). Us stock market crash risk, 1926–2010. Journal of Financial Economics, 105(2):229–259.[13] Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1- 2):167–179.[14] Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637–654.[15] Bossens, F., Rayée, G., Skantzos, N. S., and Deelstra, G. (2010). Vanna-volga methods applied to fx derivatives: from theory to market practice. International Journal of Theoretical and Applied Finance, 13(08):1293–1324.[16] Branger, N., Krautheim, E., Schlag, C., and Seeger, N. (2012). Hedging under model misspecification: All risk factors are equal, but some are more equal than others.... Journal of Futures Markets, 32(5):397–430.[17] Carr, P. and Cousot, L. (2011). A pde approach to jump-diffusions. Quantitative Finance, 11(1):33–52.[18] Carr, P. and Cousot, L. (2012). Explicit constructions of martingales calibrated to given implied volatility smiles. SIAM Journal on Financial Mathematics, 3(1):182–214.[19] Carr, P., Geman, H., Madan 5, D. B., and Yor, M. (2004). From local volatility to local lévy models. Quantitative Finance, 4(5):581–588.[20] Cheng, H.-W., Chang, L.-H., Lo, C.-L., and Tsai, J. T. (2023). Empirical performance of component garch models in pricing vix term structure and vix futures. Journal of Empirical Finance, 72:122–142.[21] Christie, A. A. (1982). The stochastic behavior of common stock variances: Value, leverage and interest rate effects. Journal of Financial Economics, 10(4):407–432.[22] Christoffersen, P. and Jacobs, K. (2004). The importance of the loss function in option valuation. Journal of Financial Economics, 72(2):291–318.[23] Christoffersen, P., Jacobs, K., and Mimouni, K. (2010). Volatility dynamics for the s&p500: Evidence from realized volatility, daily returns, and option prices. The Review of Financial Studies, 23(8):3141–3189.[24] Christoffersen, P., Jacobs, K., and Ornthanalai, C. (2012). Dynamic jump intensities and risk premiums: Evidence from s&p500 returns and options. Journal of Financial Economics, 106(3):447–472.[25] Cont, R. and Da Fonseca, J. (2002). Dynamics of implied volatility surfaces. Quantitative Finance, 2(1):45.[26] Cox, J. C., Ingersoll Jr, J. E., and Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica: Journal of the Econometric Society, pages 363–384.[27] Duffie, D., Pan, J., and Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6):1343–1376.[28] Dumas, B., Fleming, J., and Whaley, R. E. (1998). Implied volatility functions: Empirical tests. The Journal of Finance, 53(6):2059–2106.[29] Dupire, B. et al. (1994). Pricing with a smile. Risk, 7(1):18–20.[30] Garman, M. B. and Kohlhagen, S. W. (1983). Foreign currency option values. Journal ofInternational Money and Finance, 2(3):231–237.[31] Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6(2):327–343.[32] Hull, J. and White, A. (1987). The pricing of options on assets with stochastic volatilities. The Journal of Finance, 42(2):281–300.[33] Hull, J. and White, A. (2017). Optimal delta hedging for options. Journal of Banking and Finance, 82:180–190.[34] Lee, R. W. (2001). Implied and local volatilities under stochastic volatility. International Journal of Theoretical and Applied Finance, 4(01):45–89.[35] Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, pages 141–183.[36] Nandi, S. (1996). Pricing and hedging index options under stochastic volatility: an empirical examination. Technical report, Working paper.[37] Ornthanalai, C. (2014). Levy jump risk: Evidence from options and returns. Journal of Financial Economics, 112(1):69–90. zh_TW
