隨機波動模型的實作與應用

An Implementation of Stochastic Volatility Model

黃舒瑜(Shu-Yu Huang)

指導教授 ： 盧信銘

國立臺灣大學/管理學院/資訊管理學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201900044

摘要

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。

關鍵字

隨機波動模型 ； 貝氏估計 ； 馬可夫鏈蒙地卡羅

並列摘要

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.

並列關鍵字

Stochastic volatility model ； Bayesian approach ； Markov chain Monte Carlo

參考文獻

REFERENCE

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