不同高頻波動性估計量應用在風險值之績效探討及比較

Comparison of Performance of Different High Frequency Volatility Estimators, and Apply in Value at Risk.

鄭智偉(Jhih-Wei Jheng)

指導教授 ： 葉錦徽

共同指導教授 ： 丘駿飛(Jiun-Fei Chiu)

元智大學/管理學院/財務金融學系/碩士(2008年)

摘要

本文主要使用高頻資料去探討各種不同的波動性估計量在衡量風險值的表現, 我們主要比較 realized volatility, bi-power volatility, ranged-based volatility, 以及 quantile-based volatility 等四種波動性估計量。 因為他們所使用的資訊內涵不同, 所以適用於不同的經濟環境, 當外在經濟環境處於波動劇烈或是穩定持平時, 所適用的波動性估計量也不盡相同。 當經濟體系波動劇烈, 產生 jump 的機會大幅增加, 使用 realized volatility 去估算真實波動性可以幫助我們正確地預測到那些大幅損失的金融風險; 而在經濟穩定持平的時候, 使用不受 jump 影響的估計量去估算真實波動性較為適合。 從金融監理的觀點, 我們不僅藉由回溯測試去找尋哪個波動性估計量在衡量風險值有較佳的表現 , 我們也利用 expected shortfall 以及 overcharge 的觀念來探討波動性估計量的風險以及機會成本, , 方便金融管理當局評估制訂法定資本, 使用較好的風險值設定。 畢竟過於保守的法定資本會減少銀行或是金融機構的報酬率, 而過度樂觀的法定資本設定, 則無法保障一個安全健全金融體系的運作。 在監理上實務很重要的問題是一家銀行的風險值, 是直接計算比較好, 或是考量到各部門的持有資產, 利用加總風險值比較好呢? 由於沒有一個實際的企業的資料可以供我們去驗證, 所以我們使用了 ETF 作為驗證的樣本。 由金融管理當局的觀點, 使用適當的波動性估計量搭配風險值模型, 去幫助金融單位去設定適當的法定資本, 成為管理當局很重要的任務。 我們這篇研究發現 realized volatility 去衡量風險值有不錯
的表現, 在考量機會成本的情況下則發現 quantile-based volatility 則有較低的機會成本。 而直接計算風險值與加總風險值的績效表現差異不大, 這與 Berkowitz and O’brien (2002) 的
結論一致。 總結的來說, 本研究提供了政策與風險管理的重要意涵。

關鍵字

保證金設定；波動性；風險值

並列摘要

This thesis investigates the empirical properties and performance of four differentvolatility estimators constructed from high frequency asset returns: mainly realized volatility (RV), bi-power variation (BV), range-based volatility (RBV), and quantile-based volatility (QBV), in the context of Value-at-Risk. As the four es-
timators embed different content from high frequency information, they are applicable respectively under different economic environments. For example, as realized
bi-power variation captures the integrated volatility (IV) and realized volatility contains both IV and jumps, BV seems to be a good choice when economic condition is
stable while RV is more suitable for characterizing market risk in turmoil periods. Using not only the traditional backtesting methodology focusing on exceeding rate
but also an optimal perspective compromising between loss magnitudes and opportunity costs, we compare the VaR assessing performance of these volatility forecasts.
After all, setting up a VaR that is too conservative will reduce the flexibility of capital utilization of a financial institution, but a too optimistic VaR will essentially
bring disasters. We also discuss the property on the aggregation approximation of VaR of financial holding company with a basket of trading desks (positions) with
different assets: computing VaR for the firm with its market value or aggregate individual VaRs across different positions. We illustrate this issue with the ETF
of Spider due to unavailability of position data among financial institutions. Our empirical studies show that realized volatility overall has nice performance on VaR
fitness, though quantile-based volatility tends to produce VaR that generates lower opportunity cost. Moreover, consistent with that found in Berkowitz and O’brien
(2002), we found the aggregated VaR is not significantly different from using calculating a single VaR from the market value of the whole company but simply being
more tedious. We believe these new results on market risk VaR provide some important practical policy implications from the regulatory point of view towards future risk management in the financial sector/industry.

並列關鍵字

margin-setting；volatility； value at risk

參考文獻

1. Alizadeh, S., M.W. Brandt, and F.X. Diebold, 2002, Range-based estimation of stochastic volatility models, Journal of Finance 57, 1047-1091.

2. Andersen, T.G. and T. Bollerslev, 1998, Answering the skeptics: yes, standard volatility models do provide accurate forecasts, International Economic Review 39, 885-905.

3. Andersen, T.G., T. Bollerslev, F.X. Diebold, and P. Labys, 2003, Modeling and Forecasting Realized Volatility, Econometrica, 71.2, 579-625.

4. Barndorff-Nielsen, O. E. and N. Shephard, 2004a, Econometric analysis of realized covariation: high frequency covariance, regression and corre-

5. Barndorff-Nielsen, O.E. and N. Shephard, 2004b, Power and bipower variation with stochastic volatility and jumps, Journal of Financial Econometrics 2, 1-37.