1. NCCU Academic Hub
  2. Publications
  3. College of Commerce
  4. Theses
  5. Item

Publications-Theses

Article View/Open

Publication Export

Google ScholarTM

NCCU Library

Citation Infomation

Related Publications in TAIR

題名 SOFR期貨及期貨選擇權的定價與實證分析：Hull-White雙因子模型與單因子模型比較
Pricing and Empirical Analysis of SOFR Futures and Futures Options: Hull-White Two-Factor vs. One-Factor Models
作者 陳昆旻
Chen, Kun-Min
貢獻者 林士貴
Lin, Shih-Kuei
陳昆旻
Chen, Kun-Min
關鍵詞 SOFR 期貨
SOFR 期貨選擇權
Hull-White 雙因子模型
SOFR futures
SOFR futures options
Hull-White two-factor model
日期 2024
上傳時間 5-Aug-2024 12:18:44 (UTC+8)
摘要 自2017年美國替代參考利率委員會(ARRC)推薦SOFR作為美元LIBOR的替代利率以來，持續努力發展SOFR衍生性商品市場。如今，CME的SOFR期貨和期貨選擇權已成為SOFR市場上流動性最好的商品之一。本研究擴展了廣泛使用的Hull-White模型，評估了單因子和雙因子模型對SOFR期貨（線性產品）和期貨選擇權（非線性產品）定價的適用性和表現。在SOFR期貨的實證分析中，我們運用了如RMSRE、RMSE、AIC及BIC等衡量指標，並結合校準誤差來評估兩種模型。結果發現，單因子模型足以適應SOFR期貨市場的需求。對於期貨選擇權，我們最初通過蒙地卡羅模擬驗證了本文推導的（半）解析定價公式。隨後進行模型參數對波動度期限結構的敏感度分析，讓我們進一步了解不同參數對SOFR期貨選擇權波動度的影響。最後，我們發現雙因子模型在常數參數下，相較於單因子模型，更有效地捕捉了SOFR期貨選擇權的波動度期限結構。
Since the ARRC recommended SOFR as the alternative reference rate to USD LIBOR in 2017, efforts have been made to develop the SOFR derivatives market. Today, CME's SOFR futures and options are among the most liquid in the SOFR market. This study extends the widely used Hull-White model to assess both one-factor and two-factor models for pricing SOFR futures (linear products) and futures options (non-linear products). In our empirical analysis of SOFR futures, we utilized metrics such as RMSRE, RMSE, AIC, and BIC, alongside calibration errors, to evaluate the two models. The one-factor model proved adequate for the SOFR futures market. For SOFR futures options, we initially validated the (semi-)analytical pricing formulas through Monte Carlo simulation. We then conducted a sensitivity analysis of model parameters on the volatility term structure, further understanding their impact on SOFR futures options volatility. Lastly, we found that the two-factor model with constant parameters, more effectively captures the volatility term structure of SOFR futures options compared to the one-factor model.
參考文獻 Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1-2), 167–179. Black, F., & Karasinski, P. (1991). Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47(4), 52–59. Brace, A., Gellert, K., & Schlögl, E. (2024). SOFR term structure dynamics—discontinuous short rates and stochastic volatility forward rates. Journal of Futures Markets, 44(6), 936–985. Brigo, D., & Mercurio, F. (2006). Interest rate models-theory and practice: with smile, inflation and credit, volume 2. Springer. Chen, R.-R., & Scott, L. (1993). Pricing interest rate futures options with futures-style margining. Journal of Futures Markets, 13(1). Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–408. Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6), 1343–1376. Flesaker, B. (1993). Testing the Heath-Jarrow-Morton/Ho-Lee model of interest rate contingent claims pricing. Journal of Financial and Quantitative Analysis, 28(4), 483–495. Gurrieri, S., Nakabayashi, M., & Wong, T. (2009). Calibration methods of Hull-White model. Available at SSRN 1514192. Hasegawa, T. (2021). Caplet formulae for backward-looking term rates with hull-white model. Available at SSRN 3909949. Heitfield, E. & Park, Y.-H. (2019). Inferring term rates from SOFR futures prices. Available at SSRN 3134346. Henrard, M. (2018). Overnight futures: Convexity adjustment. Available at SSRN 3134346. Henrard, M. (2022). Options on overnight futures. Model Development, muRisQ Advisory, March. Henrard, M. P. (2019). Libor fallback and quantitative finance. Risks, 7(3), 88. 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. Ho, T. S., & Lee, S.-B. (1986). Term structure movements and pricing interest rate contingent claims. The Journal of Finance, 41(5), 1011–1029. Hofmann, K. F. (2020). Implied volatilities for options on backward-looking term rates. Available at SSRN 3593284. Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. The Review of Financial Studies, 3(4), 573–592. Hull, J., & White, A. (1994). Numerical procedures for implementing term structure models I: Single-factor models. Journal of Derivatives, 2(1), 7–16. Hunt, P., & Kennedy, J. (2004). Financial derivatives in theory and practice, volume 556. John Wiley and Sons. Lyashenko, A., & Mercurio, F. (2019). Looking forward to backward-looking rates: a modeling framework for term rates replacing LIBOR. Available at SSRN 3330240. Mercurio, F. (2018). A simple multi-curve model for pricing SOFR futures and other derivatives. Available at SSRN 3225872. Russo, V., & Fabozzi, F. J. (2023). Caplets/floorlets with backward-looking risk-free rates under the one-and two-factor Hull-White models. Journal of Derivatives, 31(1). Russo, V., & Torri, G. (2019). Calibration of one-factor and two-factor Hull–White models using swaptions. Computational Management Science, 16(1), 275–295. Schlögl, E., Skov, J. B., & Skovmand, D. (2023). Term structure modeling of SOFR: Evaluating the importance of scheduled jumps. Available at SSRN 4431839. Skov, J. B., & Skovmand, D. (2021). Dynamic term structure models for SOFR futures. Journal of Futures Markets, 41(10), 1520–1544. Turfus, C. (2020). Risky caplet pricing with backward-looking rates. Available at SSRN 3713880. Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.
描述 碩士
國立政治大學
金融學系
111352032
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0111352032
資料類型 thesis
dc.contributor.advisor 林士貴zh_TW
dc.contributor.advisor Lin, Shih-Kueien_US
dc.contributor.author (Authors) 陳昆旻zh_TW
dc.contributor.author (Authors) Chen, Kun-Minen_US
dc.creator (作者) 陳昆旻zh_TW
dc.creator (作者) Chen, Kun-Minen_US
dc.date (日期) 2024en_US
dc.date.accessioned 5-Aug-2024 12:18:44 (UTC+8)-
dc.date.available 5-Aug-2024 12:18:44 (UTC+8)-
dc.date.issued (上傳時間) 5-Aug-2024 12:18:44 (UTC+8)-
dc.identifier (Other Identifiers) G0111352032en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/152472-
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) 111352032zh_TW
dc.description.abstract (摘要) 自2017年美國替代參考利率委員會(ARRC)推薦SOFR作為美元LIBOR的替代利率以來，持續努力發展SOFR衍生性商品市場。如今，CME的SOFR期貨和期貨選擇權已成為SOFR市場上流動性最好的商品之一。本研究擴展了廣泛使用的Hull-White模型，評估了單因子和雙因子模型對SOFR期貨（線性產品）和期貨選擇權（非線性產品）定價的適用性和表現。在SOFR期貨的實證分析中，我們運用了如RMSRE、RMSE、AIC及BIC等衡量指標，並結合校準誤差來評估兩種模型。結果發現，單因子模型足以適應SOFR期貨市場的需求。對於期貨選擇權，我們最初通過蒙地卡羅模擬驗證了本文推導的（半）解析定價公式。隨後進行模型參數對波動度期限結構的敏感度分析，讓我們進一步了解不同參數對SOFR期貨選擇權波動度的影響。最後，我們發現雙因子模型在常數參數下，相較於單因子模型，更有效地捕捉了SOFR期貨選擇權的波動度期限結構。zh_TW
dc.description.abstract (摘要) Since the ARRC recommended SOFR as the alternative reference rate to USD LIBOR in 2017, efforts have been made to develop the SOFR derivatives market. Today, CME's SOFR futures and options are among the most liquid in the SOFR market. This study extends the widely used Hull-White model to assess both one-factor and two-factor models for pricing SOFR futures (linear products) and futures options (non-linear products). In our empirical analysis of SOFR futures, we utilized metrics such as RMSRE, RMSE, AIC, and BIC, alongside calibration errors, to evaluate the two models. The one-factor model proved adequate for the SOFR futures market. For SOFR futures options, we initially validated the (semi-)analytical pricing formulas through Monte Carlo simulation. We then conducted a sensitivity analysis of model parameters on the volatility term structure, further understanding their impact on SOFR futures options volatility. Lastly, we found that the two-factor model with constant parameters, more effectively captures the volatility term structure of SOFR futures options compared to the one-factor model.en_US
dc.description.tableofcontents 摘要 i Abstract ii Contents iii List of Figures v List of Tables vi 1 Introduction 1 1.1 Background and Motivation 1 1.2 Research Purpose 6 2 Literature Review 9 2.1 Short Rate Models 9 2.2 The Pricing of SOFR Derivatives 10 2.3 Empirical Studies on SOFR Futures Options 10 3 Methodologies 12 3.1 Hull-White Two-Factor Model 12 3.1.1 Two-Additive-Factor Gaussian Form 12 3.1.2 The Pricing of Zero-Coupon Bond 13 3.1.3 T-Forward Measure 14 3.1.4 Classical Hull-White Two-Factor Form 15 3.2 The Pricing of SOFR Futures 17 3.2.1 One-Month SOFR Futures 17 3.2.2 Three-Month SOFR Futures 18 3.3 The Pricing of SOFR Futures Options 19 3.3.1 One-Month SOFR Futures Options 20 3.3.2 Three-Month SOFR Futures Options 21 4 Empirical Results 23 4.1 Data Description 23 4.2 Calibration Procedure 25 4.3 SOFR Futures 28 4.4 SOFR Futures Options 34 4.4.1 (Semi-)Analytical and Monte Carlo Methods 34 4.4.2 Volatility Term Structure: Sensitivity Analysis 37 4.4.3 Volatility Term Structure: One-Factor vs. Two-Factor Models 39 5 Conclusions and Future Works 42 5.1 Conclusions 42 5.2 Future Works 43 References 44 Appendices 47zh_TW
dc.format.extent 1392177 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0111352032en_US
dc.subject (關鍵詞) SOFR 期貨zh_TW
dc.subject (關鍵詞) SOFR 期貨選擇權zh_TW
dc.subject (關鍵詞) Hull-White 雙因子模型zh_TW
dc.subject (關鍵詞) SOFR futuresen_US
dc.subject (關鍵詞) SOFR futures optionsen_US
dc.subject (關鍵詞) Hull-White two-factor modelen_US
dc.title (題名) SOFR期貨及期貨選擇權的定價與實證分析：Hull-White雙因子模型與單因子模型比較zh_TW
dc.title (題名) Pricing and Empirical Analysis of SOFR Futures and Futures Options: Hull-White Two-Factor vs. One-Factor Modelsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1-2), 167–179. Black, F., & Karasinski, P. (1991). Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47(4), 52–59. Brace, A., Gellert, K., & Schlögl, E. (2024). SOFR term structure dynamics—discontinuous short rates and stochastic volatility forward rates. Journal of Futures Markets, 44(6), 936–985. Brigo, D., & Mercurio, F. (2006). Interest rate models-theory and practice: with smile, inflation and credit, volume 2. Springer. Chen, R.-R., & Scott, L. (1993). Pricing interest rate futures options with futures-style margining. Journal of Futures Markets, 13(1). Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–408. Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6), 1343–1376. Flesaker, B. (1993). Testing the Heath-Jarrow-Morton/Ho-Lee model of interest rate contingent claims pricing. Journal of Financial and Quantitative Analysis, 28(4), 483–495. Gurrieri, S., Nakabayashi, M., & Wong, T. (2009). Calibration methods of Hull-White model. Available at SSRN 1514192. Hasegawa, T. (2021). Caplet formulae for backward-looking term rates with hull-white model. Available at SSRN 3909949. Heitfield, E. & Park, Y.-H. (2019). Inferring term rates from SOFR futures prices. Available at SSRN 3134346. Henrard, M. (2018). Overnight futures: Convexity adjustment. Available at SSRN 3134346. Henrard, M. (2022). Options on overnight futures. Model Development, muRisQ Advisory, March. Henrard, M. P. (2019). Libor fallback and quantitative finance. Risks, 7(3), 88. 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. Ho, T. S., & Lee, S.-B. (1986). Term structure movements and pricing interest rate contingent claims. The Journal of Finance, 41(5), 1011–1029. Hofmann, K. F. (2020). Implied volatilities for options on backward-looking term rates. Available at SSRN 3593284. Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. The Review of Financial Studies, 3(4), 573–592. Hull, J., & White, A. (1994). Numerical procedures for implementing term structure models I: Single-factor models. Journal of Derivatives, 2(1), 7–16. Hunt, P., & Kennedy, J. (2004). Financial derivatives in theory and practice, volume 556. John Wiley and Sons. Lyashenko, A., & Mercurio, F. (2019). Looking forward to backward-looking rates: a modeling framework for term rates replacing LIBOR. Available at SSRN 3330240. Mercurio, F. (2018). A simple multi-curve model for pricing SOFR futures and other derivatives. Available at SSRN 3225872. Russo, V., & Fabozzi, F. J. (2023). Caplets/floorlets with backward-looking risk-free rates under the one-and two-factor Hull-White models. Journal of Derivatives, 31(1). Russo, V., & Torri, G. (2019). Calibration of one-factor and two-factor Hull–White models using swaptions. Computational Management Science, 16(1), 275–295. Schlögl, E., Skov, J. B., & Skovmand, D. (2023). Term structure modeling of SOFR: Evaluating the importance of scheduled jumps. Available at SSRN 4431839. Skov, J. B., & Skovmand, D. (2021). Dynamic term structure models for SOFR futures. Journal of Futures Markets, 41(10), 1520–1544. Turfus, C. (2020). Risky caplet pricing with backward-looking rates. Available at SSRN 3713880. Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.zh_TW