臺灣博碩士論文加值系統

波動性可用於衡量金融資產的變動程度，其應用範疇包含風險管理、投資組合的選擇以及選擇權的定價等，因此，對投資者而言，如何準確地預測波動，成為金融領域中相當重要的課題。其中，隨機波動模型為衡量波動的一種模型，該模型將波動視為服從一個隨機過程的變量。
本研究主要探討離散時間的隨機波動模型，目的為提供一個實作基本隨機波動模型的R套件──logsv並且公開套件所有實作的相關細節。logsv所實作的模型採用馬可夫鏈蒙地卡羅估計方法。我們分別以兩組模擬資料、S&P 500、臺灣加權股價指數、美金對臺幣匯率、歐元對美金匯率等六組資料進行實驗，透過與真實值和前人研究結果的比較，檢驗模型實作的正確性。實驗結果顯示，我們所提供的logsv套件，不論是參數估計還是波動的估計，都有很好的表現。同時，利用波動估計的結果，我們討論可能引起高波動的相關金融事件或危機。

Modeling volatility becomes crucial in financial applications ranging from risk management, asset allocation to option pricing. Stochastic volatility (SV) models are one of the volatility models that treat the variances as an unobserved component following a stochastic process.
In this paper, we focus on the discrete time stochastic volatility (SV) models. We provide an R package, logsv, which implements the basic log SV model with the estimation of the Markov chain Monte Carlo approach and disclose all the implementation details. We fit the model to simulated datasets and real world datasets to test the fitness and correctness of our implementation. The experiment results with all datasets show that the estimation procedure works well on both parameter and volatility estimation. With the estimation results of the basic log SV model, we discuss some period of high volatility and highlight the financial crises and events that are potentially related.

誌謝 I
摘要 II
Abstract III
List of Figures V
List of Tables VI
1. Introduction 1
2. Literature Review 4
2.1. Basic Stochastic Volatility Models 5
2.1.1. Log Stochastic Volatility Models 5
2.1.2. Square-Root Stochastic Volatility Models 6
2.2. Extended Stochastic Volatility Models 7
2.2.1. Stochastic Volatility Models with Fat Tails 7
2.2.2. Stochastic Volatility Models with Leverage Effect 8
2.2.3. Stochastic Volatility Models with Jumps 9
2.3. Estimation of Stochastic Volatility Models 10
2.4. Implementation of Stochastic Volatility Models 12
3. Log Stochastic Volatility 13
3.1. Model 13
3.2. Algorithm 13
3.3. Implementation 20
4. Data 21
4.1. Simulated Data 21
4.2. Real World Data 22
4.3. Priors and Initial values 25
5. Estimation results 26
5.1. Results with Simulated Data 27
5.2. Results with Real World Data 29
5.2.1. Results with S&P 500 30
5.2.2. Results with TAIEX 35
5.2.3. Results with USD/TWD 38
5.2.4. Results with EUR/USD 42
6. Conclusion and Future Work 45
REFERENCE 46

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