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標題: Economic Value on Volatility Risk in Light of Jumps
作者: 林月能
關鍵字: 管理科學;應用研究
第一年計畫探討「隱含在高頻率波動度指數資料中的波動度跳躍行為」。波動度指數常被稱為投資者恐慌指數(Whaley, 2000)或市場溫度。因此,投資人可經由交易波動度指數期貨與波動度指數選擇權來進行波動度風險控管。本研究使用Lee and Mykland (2008)所發展的理論與模型檢測是否高頻率波動度指數資料含有布朗運動、小型跳躍行為、或大型跳躍行為,並將研究發現賦予投資者交易活動之經濟意義。本研究結果對於想使用隨機跳躍過程來描述波動度指數行為或想投資波動度相關產品特性的投資人或研究者有顯著地助益。本研究將指出是否使用純粹的布朗運動、或波動度跳躍、或兩者之合併可適切地描述波動度指數。為達到此研究目的,本研究需使用超高頻率之波動度指數資料。第二年計畫探討「波動度跳躍行為下的波動度風險貼水」。芝加哥交易所於2004 年5 月18 日開始交易三個月期變異數期貨。當股價含有跳躍成分時,得使用參數型模型來描述波動度交換率。本計畫探討在隨機波動度與跳躍過程下變異數期貨與波動度指數期貨價格之間的連結,並結合芝加哥交易所所計算出的波動度指數期間結構,用來描述波動度風險貼水的期間結構。第三年計畫探討「波動度指數隨機過程下之波動度指數衍生性金融商品訂價」。本計畫探討在隨機波動度與跳躍過程下,整合史丹普500 指數市場、史丹普500 指數選擇權市場、波動度期貨市場、與芝加哥交易所波動度指數期間結構來訂價波動度選擇權與探討波動度指數選擇權之應用。

Volatility Index (VIX) is known as the investor “fear index” (Whaley, 2000) inthe marketplace or the “market temperature”. The introduction of futures andoptions on VIX has been a major financial innovation that will facilitate to a greatextent the hedging of volatility risk. The first-year project uses the methodologydeveloped by Lee and Mykland (2008), which is model free, to detect if there areBrownian motion, or infinite activities (small jumps), or finite activities (big jumps)in the ultra-high frequency VIX data. This project will go nicely with the papers inthe literature, trying to model VIX with stochastic jumps. This project will pointout to which type of models researchers should focus on when valuingVIX-related products; that is, if there are purely Brownian motion, or jumps, orsome combinations in the VIX data. For this to work, the VIX data need to havea lot of depth; that is, highly traded, down to the milliseconds. The CBOElaunched the S&P 500 three-month variance futures (VT) on May 18, 2004 thatoffer an alternative to the OTC S&P 500 variance swap. VT is the firstexchange-traded contract in the U.S. to isolate pure realized variance exposurethat allows investors to cleanly trade the difference between implied and realizedvariance of the SPX over three months. The buyer of the contract is “longvolatility” and receives a payment from the seller when realized volatility is high.The seller, who is “short volatility”, benefits from a low realized volatility. Overtime index implied variance has tended to be higher than realized variance, welldocumented as the variance risk premium. To reconcile characteristic patterns ofthe term structure of variance risk premia with the term structure of varianceswap rates, this study synthesizes VT of various maturities by the CBOE VolatilityIndex (VIX) Term Structure. The second-year project presents a novel approachto estimate joint dynamics of the VIX futures market with the VT market. Whenthe stock price has jumps, the log contract fails to replicate the variance swapcontract. Hence, the usual non-parametric method fails. In order to separate thejump effect from stochastic volatility component, parametric model is necessary. The third-year project integrates CBOE VIX Term Structure with VIX futures as thenuméraire to simplify VIX option pricing in jump diffusion models of future VIXdynamics. The project introduces a model with discontinuous correlated jumpsin future VIX and future VIX volatility, and with state-dependent arrival intensity.The project discusses how to perform likelihood based inference based uponjoint VIX options/future VIX data and presents estimates of risk premiums forjump and volatility risks. The project expects to find that while complex jumpspecifications add little explanatory power in fitting VIX option data, thesemodels fare better in fitting VIX options and future VIX data simultaneously.
其他識別: NSC99-2410-H005-014-MY3
Appears in Collections:財務金融學系所

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