Vasicek 雙因子模型與卡爾曼濾波

Two-Factor Vasicek with Kalman Filter

譚景丞(Jing-Cheng Tan)

指導教授 ： 李賢源

國立臺灣大學/管理學院/財務金融學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201902162

摘要

此篇論文探討的是 Vasicek 雙因子模型的運用與如何用卡爾曼濾波器估計出多因子利率模型的參數，並對 Libor 利率進行預測與檢測套利機會。過去的研究大部分專注在如何推導公式及債券的定價模型理論。此篇論文將過去的利率模型結合工程應用的卡爾曼濾波器，通過最小化預期誤差，推算出參數，從而利用結果模型進一步預測市場利率的走勢。由於過去的研究鮮少提及模型的運用和參數的運算，此篇論文的將會把詳細步驟一一列出介紹，並在附錄附上 R code 提供參考。利率走勢的預測不僅可讓交易者作為參考的指標，同時也供債券持有金融機構等作為風險控制的一個工具。過去的風險管理工具不外乎VaR,Expected Shortfall, 資本適足率等。此篇論文也將會探討 Vasicek 模型 如何與過去風險管理工具結合並實踐到交易風險管理機制。

論文分為四個部分。第一部分介紹固定收益市場與利率曲線的變化。第二部分講述過去的研究並介紹 Vasicek 多因子模型與卡爾曼濾波器。第三部分會討論如何運用模型與工程將參數推算出來並探討市場套利空間。第四部分則結合過去風險管理工具提供一個全新的風險控管方法與概念。

關鍵字

固定收益 ； 債券 ； Libor ； 利率模型 ； 套利機會 ； Vasicek ； 風險管理 ； VaR ； Expected Shortfall ； 卡爾曼濾波器

並列摘要

This paper examines the application of mathematical models such as affine models in determining mispricing in yield curve, developing trading strategies and examining its profitability. Reliable yield curve models can be very useful in predicting and controlling risk in fixed income securities market. Most previous works focused on deriving the mathematical model and formula with little discussion about the detailed process in how to implementing the model. This paper presents a way to summarize the theoretical and practical knowledge in applying the affine models in exploring yield curve arbitrage, specifically combining Vasieck two-factor model with an engineering signal processing tool, Kalman filter, to calibrate using the real market rate data. The paper is organized as follows. The first section of this thesis discusses the major concepts of fixed income markets such as zero coupon yield curve, swap curve and arbitrage opportunities. The second section of this thesis introduces two factor Vasicek short rate models and its implications. The third section constructs trading methodology and examines its profitability. The fourth section applies the model in combining with the risk management tools such as Value at Risk and Expected Shortfall. The final section concludes this thesis.

並列關鍵字

Fixed income ； bonds ； short rate ； Libor ； yield curve ； arbitrage ； Vasicek ； Kalman filter ； risk management ； VaR ； Expected Shortfall

參考文獻

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