臺灣博碩士論文加值系統

本篇論文先介紹三類選擇權波動率模型(傳統模型、古典 SABR模型及涵蓋負利率 SABR模型)，主要討論如何以古典 SABR模型去捕捉歐洲美元選擇權的微笑曲線現象，利用兩種數值方法去較準，並做相關參數及誤差分析，提供了任意履約價波動率的報價參考。第五章則為事件研究，討論近年利率重大事件對歐洲美元選擇權波動率的影響，包含 FOMC會議、2019年附買回利率跳升及 2020年三月美國大幅降息，分析事件前後微笑曲線的移動及相關原因。

In my thesis, I will introduce three types of option volatility models (conventional models, classic SABR model, and negative rate SABR models). I mainly discuss how to use classic SABR model to capture smiling phenomenon of Eurodollar Options with two different numerical methods and analysis parameters and errors, providing a method to quote volatility with arbitrary strikes. In Chapter 5, I will study the impact of important events of interest rate change on Eurodollar options volatility. I will analysis the move of volatility smiling curves and their reasons, including FOMC, repo rate jump event in 2019 and sudden huge rate cut event happened in March 2020.

第一章 緒論……………………………………………………...1
第一節 研究背景…………………………………………………………………..1
第二節 研究動機與目的……………………………………………………….2
第二章 利率市場發展與文獻回顧 ……………………………..3
第一節 利率市場發展..………………………………………………….3
第二節 傳統模型………………………………………………………...5
第三節 古典 SABR模型………………………………………………..6
第四節 涵蓋負利率的 SABR模型……………………………………..9
第三章 研究方法………………………………………………..12
第一節 資料選擇………………………………………………………..12
第二節 模型校準過程…………………………………………………..12
第三節 事件研究方法…………………………………………………..14
第四章 模型校準結果分析…………………………………….15
第一節 校準誤差比較…………………………………………………..15
第二節 任意履約價波動率報價………………………………………..18
第五章 利率重大事件與歐洲美元選擇權波動率…………….20
第一節 FOMC會議與波動率………………………………………… 21
第二節 2019年附買回利率跳升與波動率……………………………25
第三節 2020年美國大幅降息與波動率………………………………27
第六章 結論與建議…………………………………………….35
附錄………………………………………………………………………..37
參考文獻…………………………………………………………………..41

[1] 張博能 (2016) 負利率環境下衍生性金融商品的定價
[2] 許寧翔 (2017) Heston 與 SABR 模型的比較分析及商品評價分析應用
[3] Atanasova, E.T. (2017). Pricing and Hedging Fixed Income Derivatives under Negative Interest Rates: An SABR approach
[4] Bachelier, L. (1900). The Theory of Speculation. Annales Scientifiques de l’École Normale Supérieure Mercurio, F. (2019). A Note on Building Proxy Volatility Cubes
[5] Bartlett, B. (2006). Hedging under SABR model. Wilmott Magazine, 4, 2-4
[6] Black, F., &Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 637-654
[7] Black, F. (1976). The pricing of commodity contracts. Journal of financial economics, 3(1), 167-169
[8] Black, F. (1995). Interest rate as options. Journal of finance, 50(5), 1371-1376
[9] Deloitte. 2016. Calibration and pricing using the free SABR model
https://www2.deloitte.com/content/dam/Deloitte/global/Documents/FinancialServices/gx-fsi-free-sabr.pdf Assessed Oct.11. 2019
[10] Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing Smile Risk. Wilmott Magazine, 84-108
[11] Hagan, P. S., Kumar, D., Lesniewski, A. S.,& Woodward, D. E. (2005). Probability Distribution in the SABR Model of Stochastic Volatility
[12] Hagan, P. S., Kumar, D., Lesniewski, A. S., &Woodward, D. E. (2014) Arbitrage‐Free SABR. Wilmott Magazine, 69, 60-75
[13] Hagan, P. S., Lesniewski, A. S., & Woodward, D. E. (2018). Managing Vol Surfaces (2018). Wilmott Magazine, 93, 23-43
[14] Hagan, P. S., & Lesniewski, A. S. (2019). Bartlett's Delta in the SABR Model. Wilmott Magazine, 101, 64-69
[15] Hansen, S.S. (2011). The SABR model – theory and application
[16] Jamjam, N. (2016). SABR Model Extensions For Negative Rates
[17] Jourdain, B. (2004). Loss of martingality in asset price models with lognormal stochastic volatility
[18] Kakushadze, Z. (2016). Volatility Smile as Relativistic Effect
[19] Korn, R., and Tang, S. (2013). Exact Analytical Solution for the Normal SABR Model. Wilmott Magazine, 66, 64-69
[20] Lindsay, A. E., & Brecher, D. R. (2010). Simulation of the CEV process and the local martingale property
[21] Newton’s method and optimization.
https://relate.cs.illinois.edu/course/cs357-f15/fileversion/03473f64afb954c74c02e8988f518de3eddf49a4/media/cs357-slidesnewton2.pdf Assessed Jun. 20. 2020
[22] Piiroinen, P., Roininen, L., & Simon, M. (2020). Brexit Risk Implied by the SABR Martingale Defect in the EURGBP Smile