臺灣博碩士論文加值系統

近年來，跳躍-擴散模型常被用來描述利率的變化。本論文的主要目的即以跳躍模型為基礎，提供一個預測利率及評價利率型衍生性金融商品的方法。此方法為找出跳躍的時點並將其與總體經濟或聯邦準備理事會公開市場委員會的相關事件進行對照，以找出跳躍發生的原因。實證研究發現，聯邦儲備利率的跳躍現象發生的頻率較三個月國庫券殖利率頻繁，其原因可能是因為聯邦儲備利率較易直接受聯邦儲備局公開市場操作的影響。另外，透過了解跳躍現象發生的原因也有助於評價利率選擇權。

Jump-diffusion models have been suggested to fit most interest rate processes. The aim of this thesis is to propose a procedure for forecasting the interest rate and pricing the options based on it. This procedure, considering of detecting possible jumps and relating them with economic and monetary events, is applied to the Fed funds rate and 3-month T-bill rate processes. It is seen that the proposed Gaussian-Poisson-event model fits both series better than the pure Gaussian model does. Also seen is there are more jumps in the Fed funds rate than in the yield, a result that is due to the direct impact of the Fed events to Fed funds rate. Empirical studies show that the information about jumps is helpful for the pricing of the interest rate options.

Contents

1 Introduction 1
2 Jump Models and Interest Rate 5
2.1 Jumps model used in the stock return 5
2.2 Jumps model used in the interest rate 7
3 Model Specification and Jumps detection 10
3.1 Model specification 10
3.2 Jumps detection 13
3.3 Simulation Results 14
4 Empirical Study 20
4.1 Jumps in Fed funds rate and 3-month T-bill rate 20
4.1.1 Jumps in the Fed funds rate 21
4.1.2 Jumps in 3-month T-bill rate 29
4.2 Jumps and the interest rate option pricing 34
4.2.1 In-sample IRX option pricing 35
4.2.2 Out-sample IRX option pricing 37
5 Conclusion and Discussion 40
Appendix 42
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