隱含波動度曲面對於衍生性商品的定價、造市、交易甚或是風險管理都扮演著至關重要的角色，過去有許多研究提出各式各樣的模型來描繪隱含波動度曲面的笑狀波幅與期間結構。本研究基於過去所提出的相關模型，嘗試以台指選擇權日內高頻資料做模型校準，並進而建構預測之日內隱含波動度曲面。實證結果表明，在給定日內部分資訊下，外生給定價平隱含波動度的模型相較於其他的模型在樣本外更加適應於市場的動態，並且我們的結果顯示日內隱含波動度是可預測的。最後，比較市場實際隱含波動度與我們所校準出的預測曲面，我們透過買入/賣出最被市場低估/高估的契約，建構一個delta中立的對沖策略。回測結果顯示，不考慮交易成本下，策略可獲利，佐證模型具有一定預測能力。但在考慮交易成本後，由於賺取的vega不足以支付交易成本，以致本波動度套利策略於實務上並不可行。

Implied volatility surface is very important for derivatives pricing, market making, trading or even risk management. Various models are proposed by previous studies to portray skew and term structure observed in implied volatility surfaces. In this study, we try to calibrate these models by using TAIEX options’ quotes at 1-min frequency filtered from trade book and construct predictive intraday implied volatility surfaces. Our results show that models referring to at-the-money volatility are more adaptive to the market dynamics, and it is possible for us to predict intraday volatility.
Moreover, by building a long-short delta-neutral strategy, we found that it is profitable assuming no transaction costs, which shows that our model is predictive. But after considering transaction costs, this strategy can’t work in practice since earned vega is not enough to pay transaction costs.

Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. The Review of Financial Studies, 9(1), 69–107.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654.
Carr, P., & Wu, L. (2016). Analyzing volatility risk and risk premium in option contracts: A new theory. Journal of Financial Economics, 120(1), 1–20.
Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–407.
Cox, J. C., & Ross, S. A. (1976). The valuation of options for alternative stochastic processes. Journal of financial economics, 3(1-2), 145–166.
Dumas, B., Fleming, J., & Whaley, R. E. (1998). Implied volatility functions: Empirical tests. The Journal of Finance, 53(6), 2059–2106.
Gatheral, J. (2004). A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives. Presentation at Global Derivatives & Risk Management, Madrid, 0.
Gatheral, J. (2011). The volatility surface: a practitioner’s guide. John Wiley & Sons.
Gatheral, J., & Jacquier, A. (2014). Arbitrage-free svi volatility surfaces. Quantitative Finance, 14(1), 59–71.
Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk. Wilmott, 1(8), 84–108.
Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The review of financial studies, 6(2), 327–343.
Homescu, C. (2011). Implied volatility surface: Construction methodologies and characteristics. Available at SSRN 1882567.
Matytsin, A. (1999). Modelling volatility and volatility derivatives. In Columbia practitioners conference on the mathematics of finance.
Matytsin, A. (2000). Perturbative analysis of volatility smiles. In Columbia practitioners conference on the mathematics of finance.
Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of economics and management science, 141–183.
Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of financial economics, 3(1-2), 125–144.
Stein, E. M., & Stein, J. C. (1991). Stock price distributions with stochastic volatility: an analytic approach. The review of financial studies, 4(4), 727–752.
Storn, R., & Price, K. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, 11(4), 341–359.