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| Title: | 動態隱含波動度模型：以台指選擇權為例
Dynamic Implied Volatility Functions in Taiwan Options Market |
| Authors: | 陳鴻隆
Chen,Hung Lung |
| Contributors: | 陳威光
郭維裕
Chen,Wei Kuang
Kuo,Wei Yu
陳鴻隆
Chen,Hung Lung |
| Keywords: | 隱含波動度
波動度函數
不對稱GARCH
波動度預測
delta 避險
implied volatility
volatility function
asymmetric GARCH
volatility forecasting
delta-hedged |
| Date: | 2008 |
| Issue Date: | 2009-09-14 09:33:31 (UTC+8) |
| Abstract: | 本文提出一個動態隱含波動度函數模型，以改善一般隱含波動度函數難以隨時間的經過而調整波動度曲線且無法描述資料的時間序列特性等缺點。本文模型為兩階段隱含波動度函數模型，分別配適隱含波動度函數的時間穩定(time-invariant)部分與時間不穩定(time-variant)部分。
本文模型在波動度的時間不穩定部分配適非對稱GARCH(1,1)過程，以描述隱含波動度的時間序列特性。本文使用的非對稱GARCH(1,1)過程將標的資產的正報酬與負報酬對價平隱含波動度的影響分別估計，並將蘊含於歷史價平隱含波動度中的訊息及標的資產報酬率與波動度之間的關連性藉由價平隱含波動度過程納入隱含波動度函數中，使隱含波動度函數能納入波動度的時間序列特性及資產報酬與波動度的相關性，藉此納入最近期的市場資訊，以增加隱含波動度模型的解釋及預測能力。時間穩定部分則根據Pena et al.(1999)的研究結果，取不對稱二次函數形式以配適實證上發現的笑狀波幅現象。時間穩定部分並導入相對價內外程度做為變數，以之描述價內外程度、距到期時間、及價平隱含波動度三者的交互關係；並以相對隱含波動度作為被解釋變數，使隱含波動度函數模型除理論上包含了比先前文獻提出的模型更多的訊息及彈性外，還能描繪「隱含波動度函數隨波動度的高低水準而變動」、「越接近到期日，隱含波動度對價內外程度的曲線越彎曲」、「隱含波動度函數為非對稱的曲線」、「波動度和資產價格有很高的相關性」等實證上常發現的現象。
本文以統計測度及交易策略之獲利能力檢定模型的解釋能力及預測能力是否具有統計與經濟上的顯著性。本文歸納之前文獻提出的不同隱含波動度函數模型，並以之與本文提出的模型做比較。本文以台指選擇權五分鐘交易頻率的成交價作為實證標的，以2003年1月1日~2006年12月31日作為樣本期間，並將模型解釋力及AIC作為模型樣本內配適能力之比較標準，我們發現本文提出的模型具有最佳的資料解釋能力。本文以2006年7月1日~2006年12月31日作為隱含波動度模型預測期間，以統計誤差及delta投資策略檢定模型的預測能力是否具有統計及經濟上的顯著性。實證結果指出，本文提出的模型對於預測下一期的隱含波動度及下一期的選擇權價格，皆有相當良好的表現。關於統計顯著性方面，我們發現本文提出的動態隱含波動度函數模型對於未來的隱含波動度及選擇權價格的預測偏誤約為其他隱含波動度函數模型的五分之一，而預測方向正確頻率亦高於預測錯誤的頻率且超過50%。關於經濟顯著性方面，本文使用delta投資組合進行經濟顯著性檢定，結果發現在不考慮交易成本下，本文提出的模型具有顯著的獲利能力。顯示去除標的資產價格變動對選擇權造成的影響後，選擇權波動度的預測準確性確實能經由delta投資組合捕捉；在考慮交易成本後，各模型皆無法獲得超額報酬。最後，本文提出的動態隱含波動度函數模型在考量非同步交易問題、30分鐘及60分鐘等不同的資料頻率、不同的投資組合交易策略後，整體的結論依然不變。
This paper proposes a new implied volatility function to facilitate implied volatility forecasting and option pricing. This function specifically takes the time variation in the option implied volatility into account. Our model considers the time-variant part and fits it with an asymmetric GARCH(1,1) model, so that our model contains the information in the returns of spot asset and contains the relationship of the returns and the volatility of spot asset. This function also takes the time invariant in the option implied volatility into account. Our model fits the time invariant part with an asymmetric quadratic functional form to model the smile on the volatility. Our model describes the phenomena often found in the literature, such as the implied volatility level increases as time to maturity decreases, the curvature of the dependence of implied volatility on moneyness increases as options near maturity, the implied volatility curve changes as the volatility level changes, and the implied volatility function is an asymmetric curve.
For the empirical results, we used a sample of 5 minutes transaction prices for Taiwan stock index options. For the in-sample period January 1, 2003–June 30, 2006, our model has the highest adjusted- and lowest AIC. For the out-of-sample period July 1, 2006–December 31, 2006, the statistical significance shows that our model substantially improves the forecasting ability and reduces the out-of-sample valuation errors in comparison with previous implied volatility functions. We conjecture that such good performance may be due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility. To test the economic significance of our model, we examine the profitability of the delta-hedged trading strategy based on various volatility models. We find that although these strategies are able to generate profits without transaction costs, their profits disappear quickly when the transaction costs are taken into consideration. Our conclusions were unchanged when we considered the non-synchronization problem or when we test various data frequency and different strategies. |
| Reference: | 陳威光、郭維裕、陳鴻隆 (2007)，「台指選擇權買權賣權等價理論之實證」，working paper。
陳威光、郭維裕、陳鴻隆 (2008)，「動態隱含波動度模型：無母數與有母數法之比較」，working paper。
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| Description: | 博士
國立政治大學
金融研究所
91352506
97 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0913525061 |
| Data Type: | thesis |
| Appears in Collections: | [金融學系] 學位論文
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