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題名 負利率環境下衍生性金融商品的定價
Derivative Pricing Under Negative Interest Rate Environment作者 張博能
Chang, Po Neng貢獻者 林士貴
Lin, Shih Kuei
張博能
Chang, Po Neng關鍵詞 負利率政策
利率衍生性商品定價
隨機波動度
SABR 模型
Negative Interest Rate Policy
Interest Rate Derivative Pricing
Stochastic Volatility
SABR Model日期 2016 上傳時間 20-Jul-2016 17:16:48 (UTC+8) 摘要 本篇學位論文探討在負利率環境底下的利率衍生性商品之定價模型，主要貢獻點在於藉由負利率市場資料驗證負利率定價模型的表現，並且比較傳統模型與負利率模型在正利率經濟環境的表現優劣。自從負利率政策實施以來，金融市場利率體系與定價機制已經發生深刻變化。傳統的定價模型在負利率的市場環境下無法穩定且正確的定價利率金融商品，面對新的負利率金融環境，有必要發展新的定價觀點，協助金融機構商品評價與規避利率風險。部分學者放棄傳統模型的對數常態模型假設，改採用常態模型來修正資產價格的動態過程，試圖解決負利率環境下的定價矛盾。近年來幾位學者則改採用位移對數常態模型、以及自由邊界模型來刻劃資產遠期價格的動態過程，替負利率經濟的定價理論開闢了新的一哩路。此外，穩定且正確的避險參數測量也是研究者們關心的重要議題。本論文探討幾位學者修正傳統SABR模型的觀點，進一步使用歐洲利率市場與美國利率市場的商品資料進行模型的參數校準，針對負利率環境下商品定價與風險管理上提出建議與發展方向。
Negative rate in derivatives would be discussed in our thesis. Our main contribution is to provide the empirical results for these negative pricing model by negative interest rate market data. In addition, the experiment compares the performance between traditional pricing model and these negative pricing models by positive interest rate market data. Traditional pricing model could not work effectively and consistently under negative interest rate environment. Facing the challenge of negative interest rate policy, it is quite necessary for quants to develop the new perspective of pricing financial products and view of hedging the interest rate exposure. Several studies try to use the normal distribution instead of previous convention of the log normal assumption. Recently, both shifted diffusion and free boundary model have been widely introduced in related works. Thus, these approaches bring the new concepts and inspiration for some researchers. Furthermore, the stable and correct risk metrics is also a critical issue that market participants are concerned. Three modified SABR models from different literatures would be presented and calibrated by EUR market data and USD market data in this thesis. In the long run, there are some suggestions and future studies proposed in our work for the financial product pricing and risk management in a negative interest rate capital market.參考文獻 [1] Antonov, A., Konikov, M., & Spector, M. (2015). The free boundary SABR: natural extension to negative rates. Available at SSRN 2557046.[2] Antonov,A.,Konikov,M.,&Spector,M.(2015).MixingSABRmodelsfornegativerates. Available at SSRN 2653682.[3] Antti, H. (2016). Using a normal jump-diffusion model for interest variation in a low rate and high volatility environment. Helsinki center of economic research, discussion paper, No. 402.[4] Bachelier L. (1900). Théorie de la spéculation, Annales Scientifiques de lÉcole Normale Supérieure 3 (17).[5] Bartlett, B. (2006). Hedging under SABR model. Wilmott magazine, 4, 2-4.[6] Bianchetti,M.,& Carlicchi,M (2011). Interest rates after the credit crunch: Multiple curve vanilla derivatives and sabr. Available at SSRN 1783070.[7] Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 637-654.[8] Black, F. (1976). The pricing of commodity contracts. Journal of financial economics, 3(1), 167-179.[9] Black, F. (1995). Interest rates as options. Journal of Finance, 50(5), 1371-1376.[10] Breeden, D. T., & Litzenberger, R. H. (1978). Prices of state-contingent claims implicit in option prices. Journal of business, 621-651.[11] Crispoldi, C., Wigger, G., & Larkin, P. (2015). SABR and SABR LIBOR market models in practice: with examples implemented in python. Springer.[12] Derman, E., Kani, I., & Chriss, N. (1994). Implied trinomial tress of the volatility smile. Journal of derivatives, 3(4), 7-22.[13] Dupire, B. (1994). Pricing with a smile. Risk, 7(1), 18-20.[14] Dupire, B. (1997). Pricing and hedging with smiles. Mathematics of derivative securities. Dempster and Pliska eds., Cambridge Uni. Press.[15] Hagan,P.S.,&Woodward,D.E (1999). Equivalent black volatilities. AppliedMathematical Finance, 6(3), 147-157.[16] Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk.The best of wilmott, 249.[17] Hagan, P. S., Kumar, D., Lesniewski, A., & Woodward, D. (2014). Arbitrage free SABR. Wilmott, 2014(69), 60-75.[18] Nohrouzian, H. (2015). An introduction to modern pricing of interest rate derivatives.[19] Henry-Labordére, P. (2008). Analysis, geometry, and modeling in finance: Advanced methods in option pricing. CRC Press.[20] Hull, J. C., & White, A. (2013). LIBOR vs. OIS: The derivatives discounting dilemma.Journal of investment management, forthcoming.[21] Hull,J.C.,&White,A(2014).OIS discounting, interest rate derivatives, and the modeling of stochastic interest rate spreads. Journal of investment management, forthcoming.[22] Jeanblanc, M., Yor, M., & Chesney, M. (2009). Mathematical methods for financial mar- kets. Springer Science & Business Media.[23] Frankena, L. H. (2016). Pricing and hedging options in a negative interest rate environ- ment (Doctoral dissertation, TU Delft, Delft University of Technology).[24] Oblój, J. (2007). Fine-tune your smile: Correction to Hagan et al. arXiv preprint arXiv: 0708.0998.[25] Rebonato, R., McKay, K., & White, R. (2011). The SABR/LIBOR market model: pricing, calibration and hedging for complex interest rate derivatives. John Wiley & Sons.[26] Kooiman,T(2015).Master Thesis Negative Rates in Financial Derivatives(unpublished).[27] Jönsson, M., & Sámark, U. (2016). Negative rates in a multi curve framework cap pricing and volatility transformation (unpublished).28] Jermann, U. J. (2016). Negative swap spreads and limited arbitrage. Available at SSRN. [29] van der Have, Z. (2015). Arbitrage-free methods to price European options under the SABR model (Doctoral dissertation, Delft University of Technology).[30] West,G (2005). Calibration of the SABR model in illiquid markets. Applied Mathematical Finance, 12(4), 371-385. 描述 碩士
國立政治大學
金融學系
1033520091資料來源 http://thesis.lib.nccu.edu.tw/record/#G1033520091 資料類型 thesis dc.contributor.advisor 林士貴 zh_TW dc.contributor.advisor Lin, Shih Kuei en_US dc.contributor.author (Authors) 張博能 zh_TW dc.contributor.author (Authors) Chang, Po Neng en_US dc.creator (作者) 張博能 zh_TW dc.creator (作者) Chang, Po Neng en_US dc.date (日期) 2016 en_US dc.date.accessioned 20-Jul-2016 17:16:48 (UTC+8) - dc.date.available 20-Jul-2016 17:16:48 (UTC+8) - dc.date.issued (上傳時間) 20-Jul-2016 17:16:48 (UTC+8) - dc.identifier (Other Identifiers) G1033520091 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99341 - 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) 1033520091 zh_TW dc.description.abstract (摘要) 本篇學位論文探討在負利率環境底下的利率衍生性商品之定價模型，主要貢獻點在於藉由負利率市場資料驗證負利率定價模型的表現，並且比較傳統模型與負利率模型在正利率經濟環境的表現優劣。自從負利率政策實施以來，金融市場利率體系與定價機制已經發生深刻變化。傳統的定價模型在負利率的市場環境下無法穩定且正確的定價利率金融商品，面對新的負利率金融環境，有必要發展新的定價觀點，協助金融機構商品評價與規避利率風險。部分學者放棄傳統模型的對數常態模型假設，改採用常態模型來修正資產價格的動態過程，試圖解決負利率環境下的定價矛盾。近年來幾位學者則改採用位移對數常態模型、以及自由邊界模型來刻劃資產遠期價格的動態過程，替負利率經濟的定價理論開闢了新的一哩路。此外，穩定且正確的避險參數測量也是研究者們關心的重要議題。本論文探討幾位學者修正傳統SABR模型的觀點，進一步使用歐洲利率市場與美國利率市場的商品資料進行模型的參數校準，針對負利率環境下商品定價與風險管理上提出建議與發展方向。 zh_TW dc.description.abstract (摘要) Negative rate in derivatives would be discussed in our thesis. Our main contribution is to provide the empirical results for these negative pricing model by negative interest rate market data. In addition, the experiment compares the performance between traditional pricing model and these negative pricing models by positive interest rate market data. Traditional pricing model could not work effectively and consistently under negative interest rate environment. Facing the challenge of negative interest rate policy, it is quite necessary for quants to develop the new perspective of pricing financial products and view of hedging the interest rate exposure. Several studies try to use the normal distribution instead of previous convention of the log normal assumption. Recently, both shifted diffusion and free boundary model have been widely introduced in related works. Thus, these approaches bring the new concepts and inspiration for some researchers. Furthermore, the stable and correct risk metrics is also a critical issue that market participants are concerned. Three modified SABR models from different literatures would be presented and calibrated by EUR market data and USD market data in this thesis. In the long run, there are some suggestions and future studies proposed in our work for the financial product pricing and risk management in a negative interest rate capital market. en_US dc.description.tableofcontents 1. 緒論 11.1 研究背景 11.2 研究目的 41.3 利率市場 51.4 數學工具 102. 正利率模型 142.1 Black模型 142.2 局部波動度 172.3 SABR模型 192.4 本章節結論 263. 負利率模型 273.1 常態分配模型 273.2 位移邊界模型 303.3 自由邊界模型 323.4 本章節結論 364. 模型的校準 374.1 資料與市場慣例 374.2 Cap的市場描述 38 4.3 校準波動度模型 404.4 實驗結果總整理 414.5 本章節結論 445. 結論與展望 45 zh_TW dc.format.extent 2485274 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1033520091 en_US dc.subject (關鍵詞) 負利率政策 zh_TW dc.subject (關鍵詞) 利率衍生性商品定價 zh_TW dc.subject (關鍵詞) 隨機波動度 zh_TW dc.subject (關鍵詞) SABR 模型 zh_TW dc.subject (關鍵詞) Negative Interest Rate Policy en_US dc.subject (關鍵詞) Interest Rate Derivative Pricing en_US dc.subject (關鍵詞) Stochastic Volatility en_US dc.subject (關鍵詞) SABR Model en_US dc.title (題名) 負利率環境下衍生性金融商品的定價 zh_TW dc.title (題名) Derivative Pricing Under Negative Interest Rate Environment en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Antonov, A., Konikov, M., & Spector, M. (2015). The free boundary SABR: natural extension to negative rates. Available at SSRN 2557046.[2] Antonov,A.,Konikov,M.,&Spector,M.(2015).MixingSABRmodelsfornegativerates. Available at SSRN 2653682.[3] Antti, H. (2016). Using a normal jump-diffusion model for interest variation in a low rate and high volatility environment. Helsinki center of economic research, discussion paper, No. 402.[4] Bachelier L. (1900). Théorie de la spéculation, Annales Scientifiques de lÉcole Normale Supérieure 3 (17).[5] Bartlett, B. (2006). Hedging under SABR model. Wilmott magazine, 4, 2-4.[6] Bianchetti,M.,& Carlicchi,M (2011). Interest rates after the credit crunch: Multiple curve vanilla derivatives and sabr. Available at SSRN 1783070.[7] Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 637-654.[8] Black, F. (1976). The pricing of commodity contracts. Journal of financial economics, 3(1), 167-179.[9] Black, F. (1995). Interest rates as options. Journal of Finance, 50(5), 1371-1376.[10] Breeden, D. T., & Litzenberger, R. H. (1978). Prices of state-contingent claims implicit in option prices. Journal of business, 621-651.[11] Crispoldi, C., Wigger, G., & Larkin, P. (2015). SABR and SABR LIBOR market models in practice: with examples implemented in python. Springer.[12] Derman, E., Kani, I., & Chriss, N. (1994). Implied trinomial tress of the volatility smile. Journal of derivatives, 3(4), 7-22.[13] Dupire, B. (1994). Pricing with a smile. Risk, 7(1), 18-20.[14] Dupire, B. (1997). Pricing and hedging with smiles. Mathematics of derivative securities. Dempster and Pliska eds., Cambridge Uni. Press.[15] Hagan,P.S.,&Woodward,D.E (1999). Equivalent black volatilities. AppliedMathematical Finance, 6(3), 147-157.[16] Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk.The best of wilmott, 249.[17] Hagan, P. S., Kumar, D., Lesniewski, A., & Woodward, D. (2014). Arbitrage free SABR. Wilmott, 2014(69), 60-75.[18] Nohrouzian, H. (2015). An introduction to modern pricing of interest rate derivatives.[19] Henry-Labordére, P. (2008). Analysis, geometry, and modeling in finance: Advanced methods in option pricing. CRC Press.[20] Hull, J. C., & White, A. (2013). LIBOR vs. OIS: The derivatives discounting dilemma.Journal of investment management, forthcoming.[21] Hull,J.C.,&White,A(2014).OIS discounting, interest rate derivatives, and the modeling of stochastic interest rate spreads. Journal of investment management, forthcoming.[22] Jeanblanc, M., Yor, M., & Chesney, M. (2009). Mathematical methods for financial mar- kets. Springer Science & Business Media.[23] Frankena, L. H. (2016). Pricing and hedging options in a negative interest rate environ- ment (Doctoral dissertation, TU Delft, Delft University of Technology).[24] Oblój, J. (2007). Fine-tune your smile: Correction to Hagan et al. arXiv preprint arXiv: 0708.0998.[25] Rebonato, R., McKay, K., & White, R. (2011). The SABR/LIBOR market model: pricing, calibration and hedging for complex interest rate derivatives. John Wiley & Sons.[26] Kooiman,T(2015).Master Thesis Negative Rates in Financial Derivatives(unpublished).[27] Jönsson, M., & Sámark, U. (2016). Negative rates in a multi curve framework cap pricing and volatility transformation (unpublished).28] Jermann, U. J. (2016). Negative swap spreads and limited arbitrage. Available at SSRN. [29] van der Have, Z. (2015). Arbitrage-free methods to price European options under the SABR model (Doctoral dissertation, Delft University of Technology).[30] West,G (2005). Calibration of the SABR model in illiquid markets. Applied Mathematical Finance, 12(4), 371-385. zh_TW
