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研究生: 黃子竣
Huang, Zih-Jyun
論文名稱: 運用選擇權隱含波動率預測現貨風險值 (VaR):以 G7 貨幣對為例
Forecasting FX Spot Value-at-Risk (VaR) Using Implied Volatility: Evidence from G7 Currency Pairs
指導教授: 林靖庭
Lin, Ching-Ting
口試委員: 羅秉政
丁秀儀
陳韋達
學位類別: 碩士
Master
系所名稱: 商學院 - 金融學系
Department of Money and Banking
論文出版年: 2026
畢業學年度: 114
語文別: 中文
論文頁數: 84
中文關鍵詞: 風險值隱含波動率分位數回歸集成學習深度學習
外文關鍵詞: Value-at-Risk, Implied Volatility, Quantile Regression, Ensemble Learning, Deep Learning
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  • 本研究檢驗場外外匯選擇權隱含波動率能否提升外匯現貨風險值(VaR)的樣本外預測準確性。以傳統計量、分位數回歸隱含動差(QR-IM)、集成學習與深度學習作為實證模型,建立涵蓋 G7 與 USD/TWD 共 7 個貨幣對、13 個競爭模型的跨市場比較;資料期間涵蓋 2009 年 1 月至 2025 年 12 月,以 2020 年 1 月至 2025 年 12 月為樣本外預測期,進行每日預測與回測。
    實證結果表明,價平隱含波動率係數在全部 7 個幣別中,均呈現負值且統計顯著,確認選擇權市場預期能有效估計尾部風險;集成學習模型中,LightGBM 與 CatBoost 在全部幣別均達巴塞爾綠燈評級(綠燈:250 個交易日回測窗口內突破次數不超過 4 次),且優於 QR-IM 模型與傳統計量方法,顯示隱含波動率與尾部風險之間存在非線性關係,使非線性模型較線性模型更能提升預測精準度。
    穩健性測試確認,實證結果結論對替換偏態特徵或變更天期,均維持一致。子樣本分析上,LightGBM 與 CatBoost 在 COVID-19 衝擊期與聯準會升息週期中,均維持全數貨幣對巴塞爾綠燈評級,尤其疫情期間QR-IM 模型綠燈評級數由 7 降至 5,此表現驗證了實證結果的發現。
    事件研究確認,隱含波動率前瞻預測機制在超越樣本期間的極端市場衝擊下仍維持穩健,如 2025 年解放日,尾部風險的預測依然準確。然而 2025 年臺灣央行干預方面,Granger 因果性檢定顯示 RR25(25-delta 風險逆轉)均不具對 USD/TWD 報酬率的前瞻性,揭示選擇權隱含訊號的前瞻能力在管制匯率下可能暫時失效。


    This paper examines whether over-the-counter (OTC) foreign exchange option-implied volatility improves the out-of-sample forecast accuracy of spot foreign exchange value-at-risk (VaR). Using traditional econometric, Quantile Regression Implied Moments (QR-IM), ensemble learning, and deep learning methods as empirical models, this study constructs a cross-market comparison of 13 competing models across 7 currency pairs (the G7 currencies and USD/TWD). The sample period spans January 2009 to December 2025, with January 2020 to December 2025 as the out-of-sample forecast period, over which daily forecasts and backtests are conducted.
    The empirical results show that the at-the-money implied volatility coefficient is negative and highly statistically significant across all 7 currency pairs, confirming that options' forward-looking market expectations can effectively estimate tail risk. Among the ensemble learning models, LightGBM and CatBoost achieve the Basel Green Zone rating (no more than 4 breaches within a 250-trading-day backtesting window) across all 7 currency pairs, outperforming both the QR-IM model and traditional econometric methods. This indicates a non-linear relationship between implied volatility and tail risk, such that non-linear models significantly improve forecast accuracy relative to linear models.
    Robustness tests confirm that the empirical conclusions remain consistent under feature substitution and tenor variation. In the subsample validation, LightGBM and CatBoost maintain the Basel Green Zone rating across all currency pairs during both the COVID-19 shock period and the Fed rate-hike cycle; notably, during the pandemic period, the QR-IM linear model's Green Zone count falls from 7 to 5, a result that validates the conclusion of a non-linear relationship drawn from the empirical results.
    Event studies confirm that the forward-looking transmission mechanism of implied volatility remains robust under extreme market shocks beyond the sample period, as tail-risk forecasts remain accurate during the 2025 Liberation Day episode. However, for the 2025 Taiwan central bank foreign exchange intervention, Granger causality tests show that RR25 (25-delta risk reversal) holds no significant predictive lead over USD/TWD returns, revealing that the forward-looking ability of option-implied signals may temporarily break down under a managed exchange rate regime.

    第一章 緒論 1
    第二章 文獻回顧 5
    2.1 風險值 5
    2.2 傳統計量方法 5
    2.3 選擇權波動率曲面 7
    2.3.1 隱含波動率 7
    2.3.2 場外外匯選擇權市場的報價慣例 8
    2.3.3 選擇權隱含資訊在 VaR 估計之應用 9
    2.4 條件分位數預測方法 9
    2.4.1 分位數回歸 9
    2.4.2 集成學習 10
    2.4.3 深度學習 10
    2.5 回測與監理法規 11
    2.5.1 回測 11
    2.5.2 監理法規 12
    第三章 資料 13
    3.1 資料來源 13
    3.2 即期匯率報酬率 13
    3.3 隱含波動率 14
    3.4 資料檢定 16
    第四章 方法論 17
    4.1 研究設計概覽 17
    4.2 傳統計量模型 18
    4.2.1 歷史模擬法 18
    4.2.2 RiskMetrics 19
    4.2.3 GJR-GARCH 模型 19
    4.2.4 過濾歷史模擬法(FHS-GARCH) 19
    4.2.5 隱含波動率過濾歷史模擬法(FHS-IV) 20
    4.3 分位數回歸隱含動差(QR-IM)模型 20
    4.3.1 模型架構 20
    4.3.2 基準設定 21
    4.4 集成學習模型 22
    4.4.1 訓練資料集 22
    4.4.2 隨機森林 22
    4.4.3 極端梯度提升(XGBoost) 22
    4.4.4 輕量梯度提升(LightGBM) 23
    4.4.5 類別提升(CatBoost) 23
    4.5 深度學習模型 24
    4.5.1 前饋神經網路(FFNN) 24
    4.5.2 循環神經網路(RNN) 24
    4.5.3 長短期記憶神經網路(LSTM) 25
    4.5.4 訓練設定 25
    4.6 樣本切分與超參數設定 26
    4.6.1 樣本切分 26
    4.6.2 超參數設定 27
    4.7 評估指標與回測框架 27
    4.7.1 突破比率 27
    4.7.2 統計回測框架 28
    4.7.3 巴塞爾監理框架 29
    第五章 實證結果 31
    5.1 市場特性 31
    5.2 迴歸結果 31
    5.3 預測績效 34
    5.3.1 1% 樣本外突破比率 34
    5.3.2 全分位數樣本外突破比率 38
    5.3.3 突破加總 42
    5.3.4 未突破加總 43
    5.4 回測檢定結果 45
    5.4.1 1% 樣本外回測統計檢定 46
    5.4.2 全分位數樣本外回測統計檢定 47
    5.5 巴塞爾紅綠燈監理評估 49
    5.6 綜合討論 50
    第六章 穩健性測試 52
    6.1 變動特徵 52
    6.1.1 選擇權隱含波動率 52
    6.1.2 原油波動率 54
    6.1.3 隱含買賣價差 54
    6.2 更換天期 55
    6.3 子樣本分析 57
    第七章 事件研究 60
    7.1 對等關稅衝擊 60
    7.2 臺灣央行干預 63
    第八章 結論 65
    8.1 核心發現 65
    8.2 研究限制與展望 66
    參考文獻 68
    附錄 A — 各貨幣對現貨報酬率序列與分布 71
    附錄 B — 各貨幣對波動率曲面序列與分布 75
    附錄 C — 多幣別樣本外 1% VaR 預測序列圖 79

    Bank for International Settlements. (2025, December). OTC foreign exchange turnover in April 2025 (Triennial Central Bank Survey). Bank for International Settlements.
    https://www.bis.org/statistics/rpfx25.htm
    Barone-Adesi, G., Engle, R. F., & Mancini, L. (2008). A GARCH option pricing model
    with filtered historical simulation. Review of Financial Studies, 21(3), 1223–1258.
    https://doi.org/10.1093/rfs/hhn031
    Barone-Adesi, G., Legnazzi, C., & Sala, C. (2019). Option-implied risk measures: An
    empirical examination on the S&P 500 index. International Journal of Finance & Economics, 24(4), 1409–1428. https://doi.org/10.1002/ijfe.1743
    Basel Committee on Banking Supervision. (1996). Supervisory framework for the use of
    “backtesting” in conjunction with the internal models approach to market risk capital requirements (tech. rep.). Bank for International Settlements. Basel.
    Basel Committee on Banking Supervision. (2019). Minimum capital requirements for
    market risk (tech. rep.) (Revised January 2019 (Fundamental Review of the Trading Book, FRTB)). Bank for International Settlements. Basel.
    Berkowitz, J. (2001). Testing density forecasts, with applications to risk management.
    Journal of Business & Economic Statistics, 19(4), 465–474.
    Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal
    of Political Economy, 81(3), 637–654.
    Blom, H. M., de Lange, P. E., & Risstad, M. (2023). Estimating value-at-risk in the EUR/USD currency cross from implied volatilities using machine learning methods
    and quantile regression. Journal of Risk and Financial Management, 16(7), 312.
    https://doi.org/10.3390/jrfm16070312
    Bossens, F., Rayée, G., Skantzos, N. S., & Deelstra, G. (2010). Vanna-Volga methods
    applied to FX derivatives: From theory to market practice. International Journal of Theoretical and Applied Finance, 13(8), 1293–1324. https://doi.org/10.1142/
    S0219024910006212
    Breeden, D. T., & Litzenberger, R. H. (1978). Prices of state-contingent claims implicit
    in option prices. Journal of Business, 51(4), 621–651. https://doi.org/10.1086/
    296025
    Chen, Y.-c., & Rogoff, K. (2003). Commodity currencies. Journal of International Economics, 60(1), 133–160. https://doi.org/10.1016/S0022-1996(02)00072-7
    Christoffersen, P., & Pelletier, D. (2004). Backtesting value-at-risk: A duration-based approach. Journal of Financial Econometrics, 2(1), 84–108. https://doi.org/10.1093/
    jjfinec/nbh004
    68
    Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 39(4), 841–862. https://doi.org/10.2307/2527341
    Christoffersen, P. F., Jacobs, K., & Chang, B. Y. (2013). Forecasting with option-implied
    information. In G. Elliott & A. Timmermann (Eds.), Handbook of economic forecasting (pp. 581–656, Vol. 2A). Elsevier. https://doi.org/10.1016/B978-0-444-
    53683-9.00010-4
    de Lange, P. E., Risstad, M., & Westgaard, S. (2022). Estimating value-at-risk using quantile regression and implied moments. Journal of Risk Model Validation, 16(4), 53–
    76. https://doi.org/10.21314/JRMV.2022.012
    Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk
    by regression quantiles. Journal of Business & Economic Statistics, 22(4), 367–
    381. https://doi.org/10.1198/073500104000000370
    Giot, P., & Laurent, S. (2003). Value-at-risk for long and short trading positions. Journal
    of Applied Econometrics, 18(6), 641–663. https://doi.org/10.1002/jae.710
    Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the
    expected value and the volatility of the nominal excess return on stocks. Journal of
    Finance, 48(5), 1779–1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
    Haugom, E., Ray, R., Ullrich, C. J., Veka, S., & Westgaard, S. (2016). A parsimonious
    quantile regression model to forecast day-ahead value-at-risk. Finance Research
    Letters, 16, 196–207. https://doi.org/10.1016/j.frl.2015.12.006
    Huang, A. Y., Peng, S.-P., Li, F., & Ke, C.-J. (2011). Volatility forecasting of exchange
    rate by quantile regression. International Review of Economics & Finance, 20(4),
    591–606. https://doi.org/10.1016/j.iref.2011.01.005
    Huggenberger, M., Zhang, C., & Zhou, T. (2018). Forward-looking tail risk measures
    [SSRN Working Paper No. 2909808]. https://doi.org/10.2139/ssrn.2909808
    Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities.
    The Journal of Finance, 42(2), 281–300. https://doi.org/10.1111/j.1540- 6261.
    1987.tb02568.x
    Jackwerth, J. C. (2000). Recovering risk aversion from option prices and realized returns.
    The Review of Financial Studies, 13(2), 433–451. https://doi.org/10.1093/rfs/13.
    2.433
    Jorion, P. (2001). Value at risk: The new benchmark for managing financial risk (2nd ed.).
    McGraw-Hill.
    JP Morgan/Reuters. (1996). RiskMetrics—technical document (4th ed., tech. rep.). JP
    Morgan. New York.
    Kakade, K., Jain, I., & Mishra, A. K. (2022). Value-at-risk forecasting: A hybrid ensemble
    learning GARCH-LSTM based approach. Resources Policy, 78, 102903. https :
    //doi.org/10.1016/j.resourpol.2022.102903
    69
    Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W., Ye, Q., & Liu, T.-Y. (2017).
    LightGBM: A highly efficient gradient boosting decision tree. Advances in Neural
    Information Processing Systems, 30.
    Koenker, R., & Bassett, G., Jr. (1978). Regression quantiles. Econometrica, 46(1), 33–50.
    https://doi.org/10.2307/1913643
    Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models.
    Journal of Derivatives, 3(2), 73–84. https://doi.org/10.3905/jod.1995.407942
    Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica, 41(5),
    867–887. https://doi.org/10.2307/1913811
    Nieppola, O. (2009). Backtesting value-at-risk models [Master’s thesis, Helsinki School
    of Economics].
    Nieto, M. R., & Ruiz, E. (2016). Frontiers in var forecasting and backtesting. International
    Journal of Forecasting, 32(2), 475–501. https://doi.org/10.1016/j.ijforecast.2015.
    08.003
    Ornelas, J. R. H., & Mauad, R. B. (2019). Implied volatility term structure and exchange
    rate predictability. Economics Letters, 174, 28–32. https:// doi. org/ 10. 1016/j.
    econlet.2018.10.005
    Pérignon, C., & Smith, D. R. (2010). The level and quality of value-at-risk disclosure by
    commercial banks. Journal of Banking & Finance, 34(2), 362–377. https://doi.
    org/10.1016/j.jbankfin.2009.08.009
    Taylor, J. W. (1999). A quantile regression approach to estimating the distribution of multiperiod returns. Journal of Derivatives, 7(1), 64–78. https://doi.org/10.3905/jod.
    1999.319133
    Vaidyanathan, K. (2012). An FX options model that incorporates 25-delta strangles and
    25-delta risk reversals. International Journal of Financial Markets and Derivatives, 3(1), 20–35.
    Zhang, G., Patuwo, B. E., & Hu, M. Y. (1998). Forecasting with artificial neural networks:
    The state of the art. International Journal of Forecasting, 14(1), 35–62. https ://doi.org/10.1016/S0169-2070(97)00044-7
    Zhang, Y., & Nadarajah, S. (2018). A review of backtesting for value at risk. Communications in Statistics—Theory and Methods, 47(15), 3616–3639. https://doi.org/10.1080/03610926.2017.1361984
    金融監督管理委員會銀行局. (2026). 本國金控集團國內及海外暴險 (季) 統計表.

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