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| Title: | 透過帶有跳躍的Hull and White短期利率模型建構SOFR模型
Modeling The SOFR Using Hull and White Short Rate Model with Jump Diffusions |
| Authors: | 陳昱丞
Chen, Yu-Cheng |
| Contributors: | 廖四郎
Liao, Szu-Lang
陳昱丞
Chen, Yu-Cheng |
| Keywords: | Hull-White模型
跳躍
SOFR利率
移動窗格法
粒子群最佳化演算法
Hull-White model
Jump
SOFR rate
Moving window approach
Particle swarm optimization algorithm |
| Date: | 2023 |
| Issue Date: | 2023-07-06 16:44:39 (UTC+8) |
| Abstract: | 本研究旨在探索金融市場利率模型中參數估計方法，並應用於含有跳躍項的
Hull-White 模型，我們採用移動窗格法結合粒子群最佳化演算法對模型參數進行估計，研究分為兩種情形進行討論。
第一種情形，我們觀測到參數隨時間推進而改變，在利率估計方面有較高準確性，通過每個時間窗格進行參數的重新估計，模型能夠更好的適應市場的動態變化與不穩定性。第二種情形，我們採取相同的參數估計方式，但選擇平均均方根誤差最小的參數集作為模型參數，並用於估計所有時間點的利率。此法對於利率的估計非常依賴參數集訓練的數據狀態，在相對平穩的市場環境中，此法能夠提供準確的跳躍後平穩期利率估計，反之在相對動盪的市場環境中，此法能夠提供出色的跳躍時利率估計。
研究結果表明參數估計所使用的資料，對於後續預估有很大的影響，若欲固定參數估計後續利率時，建議加入總經資料，如聯準會（FED）升息通知等等。這樣有利於改變參數的選擇，以提升估計的準確度。
This study aims to explore parameter estimation methods in financial market interest rate models, specifically applied to the Hull-White model with jump components. We employ a moving window approach combined with particle swarm optimization algorithm to estimate the model parameters.
The study is divided into two scenarios for discussion. In the first scenario, we observe that the parameters change over time, resulting in higher accuracy in interest rate estimation. By re-estimating the parameters in each time window, the model can better adapt to the dynamic changes and instability of the market. In the second scenario, we use the same parameter estimation method but select the parameter set with the minimum average root mean square error as the model parameters for estimating rates at all time points. This method heavily relies on the data state in the training of the parameter set. In relatively stable market environments, this approach provides accurate estimation of post-jump steady-state rates. Conversely, in relatively volatile market environments, it offers excellent estimation of jump-timerates.
The results demonstrate the significant impact of the data used for parameter estimation on subsequent forecasting. To improve estimation accuracy when fixing parameter estimates for subsequent rates, it is recommended to incorporate macroeconomic data, such as Federal Reserve (FED) rate hike notifications. This enables better parameter selection and enhances estimation accuracy. |
| Reference: | 1. Ahn, C. M., & Thompson, H. E. (1988). Jump-diffusion Processes and the Term Structure of Interest Rates. Journal of Finance, 43(1), 155-174.
2. Baz, J., & Das, S. R. (1996). Analytical Approximations of the Term Structure for Jump-Diffusion Process: A Numerical Analysis. The Journal of Fixed Income, 6(1),
78-86.
3. Baz, J., & Das, S. R. (1999). Jump Processes in Financial Markets and Macroeconomy: Stylized Facts and Empirical Evidence. Journal of Economic Surveys, 13(4), 397-416.
4. Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A Theory of the Term Structure of Interest Rates. Econometrica, 53(2), 385-407.
5. Duffie, D., Pan, J., Singleton K. (2000). Transform Analysis and Asset Pricing for Affine Jump-Diffusions. Econometrica, 68(6), 1343-1376.
6. Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5(2), 177-188.
7. Hull, J., & White, A. (1990). Pricing Interest Rate Derivative Securities. Review of Financial Studies, 3(4), 573-592.
8. Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. In Proceedings of IEEE International Conference on Neural Networks, 4, 1942-1948.
9. Ramkisoensing, A. (2016). Simplicity vs. Complexity: Jump Diffusions in Affine Term Structure [Unpublished Master’s Thesis]. Erasmus University of Rotterdam.
https://www.semanticscholar.org/paper/Simplicity-vs.-Complexity%3A-JumpDiffusions-in-A%EF%AC%83neRamkisoensing/9d4beacdc5ff352db50205a8140c7e6edbfd033b.
10. Shi, Y. & Eberhart, R. C. (1998). Parameter Selection in Particle Swarm Optimization. Evolutionary Programming VII, 591-600.
11. Skov, J. B., & Skovmand, D. (2021). Dynamic Term Structure Models for SOFR Futures. The Journal of Futures Markets, 41, 1520-1544.
12. Xu, M. (2021). SOFR Derivative Pricing Using a Short Rate Model. The European Journal of Finance [Unpublished Mater’s Thesis]. American International Group, Inc. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4007604.
13. Zhou, J., Liu, C., Tian, Y., He, X., & Ge, X. (2021). Using Particle Swarm Optimization Algorithm to Calibrate the Term Structure Model. Mathematical Problems in Engineering, 2021. |
| Description: | 碩士
國立政治大學
金融學系
109352013 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109352013 |
| Data Type: | thesis |
| Appears in Collections: | [金融學系] 學位論文
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