隱含波動率曲面變動之預測分析-利用台指選擇權之實證

Predictable Dynamics in the TAIEX Option Implied Volatility Surface

黃泰霖(Tie-Lin Huang)

指導教授 ： 謝文良

淡江大學/商學院/財務金融學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00375

摘要

本研究的主要目的為探討隱含波動率曲面是否具有可預測的效果，參照Goccalves and Guidolin (2006)所使用的VAR兩階段預測方式，對台指選擇權進行實證。

首先對每日在市場交易的選擇權之隱含波動率配適平滑公式，以價性、
到期期間為解釋變數，隱含波動率為被解釋變數，利用簡單迴歸估計出平滑公式的係數，並將所求出來的係數代入VAR模型對迴歸係數做預測，再利用修正過的迴歸係數做為更新平滑公式的係數，並且對隱含波動率曲面做預測，探討相同的預測方式在台指選擇權是否依然具有預測的效果。

實證結果發現，利用平滑公式配適隱含波動率所得到的係數，會隨著時間變動而變化，具有隨狀態時間改變的性質。利用二階段的預測方式，可以增加橫斷面模型對隱含波動率曲面的配適效果，隱含波動率曲面具有可預測性；然而隨著預測的期間增加，預測曲面的效果會迅速降低，甚至產生對係數過度配適的問題。

關鍵字

隱含波動率 ； 隱含波動率曲面 ； 向量自我迴歸模型 ； 隱含波動微笑

並列摘要

One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time.
In this paper we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the TAIEX option IVS. In the first stage we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas et al. (1998). In the second-stage we model the dynamics of the cross-sectional first-stage implied volatility surface coefficients by means of vector autoregression models.
We find that not only the TAIEX implied volatility surface can be success fully modeled, but also that its movements over time are predictable in a statistical sense. However, when the fitted implied volatileity surface one week later, the VAR-type model’s prediction errors grow larger than another. The time passing is an important cause of overfitting at the movements of IVS.

並列關鍵字

implied volatility surface ； implied volatility function ； implied volatileity smile ； option pricing

參考文獻

杜化宇 (Anthony H. Tu) 任紀為 (Chi-Wei Jen)，外匯選擇權的定價與馬可夫鏈蒙地卡羅法的應用，風險管理學報 第七卷 第三期 2005年 11月

Bakshi G., C., Cao and Z., Chen, (1997), .“Empirical Performance of Alternative Option Pricing Models.”, Journal of Finance, 52, 2003-2049.

Bates, D. S. (1996). “Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options.” Review of Financial Studies, Vol. 9, pp.69-108.

Black, F., and M., Scholes, (1973), .“The Pricing of Options and Corporate Liabilities., Journal of Political Economy”, 81, 637-654.

Bollen, N.P., and R. E. Whaley (2004) , “Does net buying pressure affect the shape of implied volatility function?,” Journal of Finance, 59, pp.711-753.