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題名 深度校準：以G2++ 利率模型為例
Calibrating G2++ Interest Rate Model : an Artificial Neural Network approach作者 楊東翰
Yang, Tung-Han貢獻者 廖四郎
Liao, Szu-Lang
楊東翰
Yang, Tung-Han關鍵詞 校準
最佳化
利率模型
類神經網路
深度學習
Calibration
Optimization
Interest rate model
Artificial Neural Network
Deep learning日期 2019 上傳時間 7-Aug-2019 16:11:38 (UTC+8) 摘要 校準一直是金融工程領域中的重要課題。評估定價模型實務上的可行性，主要端看模型是否具有校準市場資訊的能力。傳統上，執行校準需要反覆進行商品定價，而定價上牽涉的資產動態過程離散化與模擬，可能的龐大計算量將導致校準非常耗時且無效率。本研究提出的「深度校準」乃是基於深度學習框架下的校準方法，旨在解決校準實務上速度緩慢的問題。本研究以G2++ 模型為例，利用類神經網路模型「深度學習」利率模型的定價過程，將傳統校準所牽涉的繁複計算囊括在類神經網路模型的訓練階段，待模型訓練完畢後，即可無需反覆進行耗時的定價過程，從而提升校準流程的效率。為了讓深度校準實務上的應用更一般化，本研究建構的類神經網路模型，可同時校準市場上價平利率交換選擇權與價平利率上限隱含波動度報價。實證結果顯示，深度校準可將原先所需的十分鐘降至一秒以內，且無論是校準誤差或定價誤差上，其結果與傳統校準相近。再者，深度校準的穩健性相當高，無論是面對不同校準商品、不同貨幣市場乃至不同最佳化演算法，深度校準皆能維持既有的成效。本研究另檢驗了實務上看重的模型再訓練週期，推論本研究的類神經網路每兩個禮拜需要重新訓練一次。最後，本研究總結了深度校準的實務上的優點，對於深度校準「快速又不失精確度」的優良特性，本研究亦給予合理推論。
Calibration is an important topic in the field of financial engineering. The implementation of pricing models requires the calibration of model parameters to observed market data. Traditionally, model calibration routines involve repetitive pricing of financial instruments, making calibration of many interest rate models expensive and inefficient, since the dynamics of the underlying asset can be approximated by costly discretization for the simulation. We present a deep-learning-based calibration method called “deep calibration” to resolve the slow calibration issue that practitioners face in practice. In this work we propose a procedure for deep calibration of G2++ model. We evaluate the efficiency of standard calibration procedure by training an artificial neural network to “deeply learn” the complex pricing function, off-loading the bulk of calculations to a training phase. To provide a general implementation of deep calibration, we present a specific architecture that is built to calibrate at-the-money swaption volatilities and at-the-money cap volatilities simultaneously. Experiments show that deep calibration procedure performs the calibration task in a fraction of a second, compared with 10 minutes taken by standard calibration procedure. Moreover, deep calibration procedure performs as well as standard calibration in both calibration error and pricing error. In addition, we examine the robustness by presenting deep calibration with respect to different financial instruments, pricing currencies and optimizers and confirm the sustained high performance of our approach. We also examine the cycle of model retraining. Based on our findings, we conclude that the trained neural network should be retrained 2 weeks. Finally, we investigate the advantages and the reason for the “high accuracy and speed” characteristic provided by deep calibration.參考文獻 [1] Abadi, M. et al. (2016). “Tensorflow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467.[2] Bayer, C. & B. Stemper (2018). “Deep Calibration of Rough Stochastic Volatility Models,” arXiv:1810.03399.[3] Bayer, C., P. Friz & J. Gatheral (2016). “Pricing Under Rough Volatility,” Quantitative Finance, 16 (6), 887-904.[4] Bottou, L. (2012). “Stochastic Gradient Descent Tricks,” Springer Berlin Heidelberg.[5] Boyd, S. & L. Vandenberghe (2004), “Convex Optimization,” Cambridge University Press.[6] Brigo, D. & F. Mercurio (2006). “Interest Rate Models: Theory and Practice - with Smile, Inflation and Credit,” Springer Berlin Heidelberg.[7] Cybenko, G. (1989). “Approximation by Superpositions of a Sigmoidal Function,” Mathematics of Control, Signals, and Systems, 2 (4), 303-314.[8] De Spiegeleer, J., D. B. Madan, S. Reyners, & W. Schoutens (2018). “Machine Learning for Quantitative Finance: Fast Derivative Pricing, Hedging and Fitting,” Journal of Quantitative Finance, 18 (10), 1635-1643.[9] Duchi, J., E. Hazan, & Y. Singer (2011). “Adaptive Subgradient Methods for Online Learning and Stochastic Optimization,” The Journal of Machine Learning Research, 12, 2121-2159.[10] Garcia, R. & R. Gençay (2000). “Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint,” Journal of Econometrics, 94 (1–2), 93-115.[11] Gatheral, J. (2017). ‘Rough Volatility: An Overview,’ Global Derivatives Trading and Risk Management (Barcelona Presentation).[12] Goodfellow , I., Y. Bengio & A. Courville (2016). “Deep Learning,” MIT Press.[13] Gurrieri, S., M. Nakabayashi & T. Wong (2009). “Calibration Methods of Hull-White Model,” Available at SSRN: https://ssrn.com/abstract=1514192.[14] Hernandez, A.. (2016). “Model Calibration with Neural Networks,” Risk.[15] Hernandez, A.. (2017). “Model Calibration: Global Optimizer vs. Neural Network,” Available at SSRN: https://ssrn.com/abstract=2996930.[16] Hornik, K., M. Stinchcombe and H. White (1990), “Universal Approximation of an Unknown Mapping and Its Derivatives Using Multilayer Feedforward Networks,” Neural Networks, 3 (5), 551-560.[17] Hull, J. & A. White (1994). “Numerical Procedures for Implementing Term Structure Models II: Two-Factor Models,” Journal of Derivatives, 2 (2), 37-48.[18] Hutchinson, J., A. Lo & T. Poggio (1994). “A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks,” Journal of Finance, 49 (3), 851-889.[19] Klos, M. and Z. Waszczyszyn (2011). “Modal Analysis and Modified Cascade Neural Networks in Identification of Geometrical Parameters of Circular Arches,” Computers and Structures, 89 (7), 581-589[20] Levenberg, K. (1944). “A Method for the Solution of Certain Non-Linear Problems in Least Squares,” Quarterly of Applied Mathematics, 2, 164-168.[21] Levendorskii, S. (2004). “Consistency Conditions for Affine Term Structure Models,” Stochastic Processes and their Applications, 109 (2), 225-261.[22] Liu, S., A. Borovykh, L. A. Grzelak, & C. W. Oosterlee (2019). “A Neural Network-Based Framework for Financial Model Calibration,” arXiv:1904.10523.[23] Marquardt, D. (1963). “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” Journal on Applied Mathematics, 11 (2), 431-441.[24] Nocedal, J. & S. Wright (2006). “Numerical Optimization,” Springer New York.[25] QuantLib: A free/open-source library for quantitative finance, Available online at: http://www.quantlib.org.[26] Rogers, C. (1995). “Which Model for the Term Structure Should One Use?” Mathematical Finance, 65, 93-116.[27] Rumelhart, D. E., G. E. Hinton & R. J. Williams (1986). “Learning Representations by Back-Propagating Errors”, Nature, 323 (6088), 533–536.[28] Storn, R. and K. Price (1997). “Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces,” Journal of Global Optimization, 11 (4), 341–359.[29] TensorFlow: An end-to-end open source machine learning platform, Available online at: https://www.tensorflow.org/.[30] Vollrath, I. & J. Wendland (2009). “Calibration of Interest Rate and Option Models Using Differential Evolution,” Available at SSRN: https://ssrn.com/abstract=1367502.[31] Yao, J., Y. Li, C. L. Tan (2000). “Option Price Forecasting Using Neural Networks,” Omega, 28 (4), 455-466.[32] Zaw, K., G. R. Liu, B. Deng, & K. B. C. Tan (2009). “Rapid Identification of Elastic Modulus of the Interface Tissue on Dental Implants Surfaces Using Reduced-Basis Method and a Neural Network,” Journal of Biomechanics, 42, 634-641.[33] Zhang, L., L. Li, H. Ju, & B. Zhu (2010). “Inverse Identification of Interfacial Heat Transfer Coefficient Between the Casting and Metal Mold Using Neural Network,” Energy Conversion and Management, 51, 1898-1904. 描述 碩士
國立政治大學
金融學系
106352030資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106352030 資料類型 thesis dc.contributor.advisor 廖四郎 zh_TW dc.contributor.advisor Liao, Szu-Lang en_US dc.contributor.author (Authors) 楊東翰 zh_TW dc.contributor.author (Authors) Yang, Tung-Han en_US dc.creator (作者) 楊東翰 zh_TW dc.creator (作者) Yang, Tung-Han en_US dc.date (日期) 2019 en_US dc.date.accessioned 7-Aug-2019 16:11:38 (UTC+8) - dc.date.available 7-Aug-2019 16:11:38 (UTC+8) - dc.date.issued (上傳時間) 7-Aug-2019 16:11:38 (UTC+8) - dc.identifier (Other Identifiers) G0106352030 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/124734 - 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) 106352030 zh_TW dc.description.abstract (摘要) 校準一直是金融工程領域中的重要課題。評估定價模型實務上的可行性，主要端看模型是否具有校準市場資訊的能力。傳統上，執行校準需要反覆進行商品定價，而定價上牽涉的資產動態過程離散化與模擬，可能的龐大計算量將導致校準非常耗時且無效率。本研究提出的「深度校準」乃是基於深度學習框架下的校準方法，旨在解決校準實務上速度緩慢的問題。本研究以G2++ 模型為例，利用類神經網路模型「深度學習」利率模型的定價過程，將傳統校準所牽涉的繁複計算囊括在類神經網路模型的訓練階段，待模型訓練完畢後，即可無需反覆進行耗時的定價過程，從而提升校準流程的效率。為了讓深度校準實務上的應用更一般化，本研究建構的類神經網路模型，可同時校準市場上價平利率交換選擇權與價平利率上限隱含波動度報價。實證結果顯示，深度校準可將原先所需的十分鐘降至一秒以內，且無論是校準誤差或定價誤差上，其結果與傳統校準相近。再者，深度校準的穩健性相當高，無論是面對不同校準商品、不同貨幣市場乃至不同最佳化演算法，深度校準皆能維持既有的成效。本研究另檢驗了實務上看重的模型再訓練週期，推論本研究的類神經網路每兩個禮拜需要重新訓練一次。最後，本研究總結了深度校準的實務上的優點，對於深度校準「快速又不失精確度」的優良特性，本研究亦給予合理推論。 zh_TW dc.description.abstract (摘要) Calibration is an important topic in the field of financial engineering. The implementation of pricing models requires the calibration of model parameters to observed market data. Traditionally, model calibration routines involve repetitive pricing of financial instruments, making calibration of many interest rate models expensive and inefficient, since the dynamics of the underlying asset can be approximated by costly discretization for the simulation. We present a deep-learning-based calibration method called “deep calibration” to resolve the slow calibration issue that practitioners face in practice. In this work we propose a procedure for deep calibration of G2++ model. We evaluate the efficiency of standard calibration procedure by training an artificial neural network to “deeply learn” the complex pricing function, off-loading the bulk of calculations to a training phase. To provide a general implementation of deep calibration, we present a specific architecture that is built to calibrate at-the-money swaption volatilities and at-the-money cap volatilities simultaneously. Experiments show that deep calibration procedure performs the calibration task in a fraction of a second, compared with 10 minutes taken by standard calibration procedure. Moreover, deep calibration procedure performs as well as standard calibration in both calibration error and pricing error. In addition, we examine the robustness by presenting deep calibration with respect to different financial instruments, pricing currencies and optimizers and confirm the sustained high performance of our approach. We also examine the cycle of model retraining. Based on our findings, we conclude that the trained neural network should be retrained 2 weeks. Finally, we investigate the advantages and the reason for the “high accuracy and speed” characteristic provided by deep calibration. en_US dc.description.tableofcontents 目錄第一章 緒論 1第一節 研究背景與動機 1第二節 研究目的 2第三節 研究架構 3第二章 文獻探討 4第一節 利率模型演進 4第二節 深度學習應用於參數校準 11第三章 參數校準 13第一節 校準概述 13第二節 校準目標 14第三節 校準方法 15第四節 校準策略 26第四章 研究方法 28第一節 深度學習 28第二節 深度校準 34第三節 研究對象 37第四節 研究模型 41第五章 實證結果 50第一節 利率交換選擇權波動度之深度校準 51第二節 利率上限波動度之深度校準 61第六章 結論與建議 68第一節 研究結論 68第二節 未來建議 69參考文獻 71 zh_TW dc.format.extent 2311711 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106352030 en_US dc.subject (關鍵詞) 校準 zh_TW dc.subject (關鍵詞) 最佳化 zh_TW dc.subject (關鍵詞) 利率模型 zh_TW dc.subject (關鍵詞) 類神經網路 zh_TW dc.subject (關鍵詞) 深度學習 zh_TW dc.subject (關鍵詞) Calibration en_US dc.subject (關鍵詞) Optimization en_US dc.subject (關鍵詞) Interest rate model en_US dc.subject (關鍵詞) Artificial Neural Network en_US dc.subject (關鍵詞) Deep learning en_US dc.title (題名) 深度校準：以G2++ 利率模型為例 zh_TW dc.title (題名) Calibrating G2++ Interest Rate Model : an Artificial Neural Network approach en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Abadi, M. et al. (2016). “Tensorflow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467.[2] Bayer, C. & B. Stemper (2018). “Deep Calibration of Rough Stochastic Volatility Models,” arXiv:1810.03399.[3] Bayer, C., P. Friz & J. Gatheral (2016). “Pricing Under Rough Volatility,” Quantitative Finance, 16 (6), 887-904.[4] Bottou, L. (2012). “Stochastic Gradient Descent Tricks,” Springer Berlin Heidelberg.[5] Boyd, S. & L. Vandenberghe (2004), “Convex Optimization,” Cambridge University Press.[6] Brigo, D. & F. Mercurio (2006). “Interest Rate Models: Theory and Practice - with Smile, Inflation and Credit,” Springer Berlin Heidelberg.[7] Cybenko, G. (1989). “Approximation by Superpositions of a Sigmoidal Function,” Mathematics of Control, Signals, and Systems, 2 (4), 303-314.[8] De Spiegeleer, J., D. B. Madan, S. Reyners, & W. Schoutens (2018). “Machine Learning for Quantitative Finance: Fast Derivative Pricing, Hedging and Fitting,” Journal of Quantitative Finance, 18 (10), 1635-1643.[9] Duchi, J., E. Hazan, & Y. Singer (2011). “Adaptive Subgradient Methods for Online Learning and Stochastic Optimization,” The Journal of Machine Learning Research, 12, 2121-2159.[10] Garcia, R. & R. Gençay (2000). “Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint,” Journal of Econometrics, 94 (1–2), 93-115.[11] Gatheral, J. (2017). ‘Rough Volatility: An Overview,’ Global Derivatives Trading and Risk Management (Barcelona Presentation).[12] Goodfellow , I., Y. Bengio & A. Courville (2016). “Deep Learning,” MIT Press.[13] Gurrieri, S., M. Nakabayashi & T. Wong (2009). “Calibration Methods of Hull-White Model,” Available at SSRN: https://ssrn.com/abstract=1514192.[14] Hernandez, A.. (2016). “Model Calibration with Neural Networks,” Risk.[15] Hernandez, A.. (2017). “Model Calibration: Global Optimizer vs. Neural Network,” Available at SSRN: https://ssrn.com/abstract=2996930.[16] Hornik, K., M. Stinchcombe and H. White (1990), “Universal Approximation of an Unknown Mapping and Its Derivatives Using Multilayer Feedforward Networks,” Neural Networks, 3 (5), 551-560.[17] Hull, J. & A. White (1994). “Numerical Procedures for Implementing Term Structure Models II: Two-Factor Models,” Journal of Derivatives, 2 (2), 37-48.[18] Hutchinson, J., A. Lo & T. Poggio (1994). “A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks,” Journal of Finance, 49 (3), 851-889.[19] Klos, M. and Z. Waszczyszyn (2011). “Modal Analysis and Modified Cascade Neural Networks in Identification of Geometrical Parameters of Circular Arches,” Computers and Structures, 89 (7), 581-589[20] Levenberg, K. (1944). “A Method for the Solution of Certain Non-Linear Problems in Least Squares,” Quarterly of Applied Mathematics, 2, 164-168.[21] Levendorskii, S. (2004). “Consistency Conditions for Affine Term Structure Models,” Stochastic Processes and their Applications, 109 (2), 225-261.[22] Liu, S., A. Borovykh, L. A. Grzelak, & C. W. Oosterlee (2019). “A Neural Network-Based Framework for Financial Model Calibration,” arXiv:1904.10523.[23] Marquardt, D. (1963). “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” Journal on Applied Mathematics, 11 (2), 431-441.[24] Nocedal, J. & S. Wright (2006). “Numerical Optimization,” Springer New York.[25] QuantLib: A free/open-source library for quantitative finance, Available online at: http://www.quantlib.org.[26] Rogers, C. (1995). “Which Model for the Term Structure Should One Use?” Mathematical Finance, 65, 93-116.[27] Rumelhart, D. E., G. E. Hinton & R. J. Williams (1986). “Learning Representations by Back-Propagating Errors”, Nature, 323 (6088), 533–536.[28] Storn, R. and K. Price (1997). “Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces,” Journal of Global Optimization, 11 (4), 341–359.[29] TensorFlow: An end-to-end open source machine learning platform, Available online at: https://www.tensorflow.org/.[30] Vollrath, I. & J. Wendland (2009). “Calibration of Interest Rate and Option Models Using Differential Evolution,” Available at SSRN: https://ssrn.com/abstract=1367502.[31] Yao, J., Y. Li, C. L. Tan (2000). “Option Price Forecasting Using Neural Networks,” Omega, 28 (4), 455-466.[32] Zaw, K., G. R. Liu, B. Deng, & K. B. C. Tan (2009). “Rapid Identification of Elastic Modulus of the Interface Tissue on Dental Implants Surfaces Using Reduced-Basis Method and a Neural Network,” Journal of Biomechanics, 42, 634-641.[33] Zhang, L., L. Li, H. Ju, & B. Zhu (2010). “Inverse Identification of Interfacial Heat Transfer Coefficient Between the Casting and Metal Mold Using Neural Network,” Energy Conversion and Management, 51, 1898-1904. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU201900253 en_US
