快速傅利葉轉換下的選擇權訂價模型-以台指選擇權為例

Empirical Comparison of Alternative Option Pricing Models Using Fast Fourier Transform: Evidence from TAIEX Options market.

黃昱仁(Yu-Ren Huang)

指導教授 ： 林允永

共同指導教授 ： 李進生(Chin-Shen Lee)

淡江大學/商學院/財務金融學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00100

摘要

台指選擇權近年來已逐漸發展成一成熟市場。本文採用快速傅利葉轉換的方法，比較 Heston (1993)年的連續型隨機波動率模型、VG模型、Ad Hoc BS 模型及BS 等四個模型。
實証結果顯示，MAE與MAPE在樣本外一日近月買權的訂價效率以AHBS 模型最好，遠月及整體部份大致以SV模型表現較好。而樣本外七日除了近、遠月及整體的深價內買權以VG模型表現較優外，其餘大部分仍以SV模型表現最好。RMSE則顯示除了樣本外七日遠月無一致性結論外，其他幾乎以SV模型最小，顯示SV模型的誤差穩性性。此外，MPE顯示SV模型有高估價外買權及價內賣權並低估價內買權及價外賣權的傾向，此種風險中立機率集中於左尾的表現，推估原因與波動率和標的資產報酬率之相關係數為負值有關。
誤差來源分析部份，採用的誤差因子包括價性、價性平方項、到期期間與利率。實證結果顯示，除了樣本外七日賣權在價性及利率等兩項因子之迴歸斜率係數不顯著外，其餘係數皆顯著。同時也發現SV模型可以改善波動率微笑。

關鍵字

快速傅利葉轉換 ； Heston ； 隨機波動率 ； VG ； 定態波動率 ； 誤差分析

並列摘要

In the last decade, TXO has become one of the most famous trading derivatives. This article compares empirical performances of four option pricing models: (1). Heston’s continuous-time stochastic volatility model, (2). Madan et al.’s variance gamma model, (3).Dumas et al.’s ad hoc BS model, and (4). BS model.
Our empirical results for one day ahead out–of-sample show that near-month call options perform best, while SV model outperforms the others in the all sample case and forward month case. For one week ahead out–of-sample performances, I find that except deep out- and out-of-the money near-month put options and call options, VG model shows the best performances in deep-in-the-money contracts and SV the others. We also find that SV model generally has min RMSE values that mean large pricing error occurs least. However, we can see SV model also overprices out-of-the-money calls and in-the-money puts and underprices out-of-the-money puts and in-the-money calls from MPE. This type of mispricing indicates an unusual concentration of probability mass in the left tail of the risk neutral distribution of the index returns, part of which can result from negative correlation between index returns and volatility.
In terms of error regression analysis, after taking into account the four error factors (maturity, interest, moneyness and its square term), all slope parameters are significant except moneyness and interest rate in one week ahead put options. Otherwise, we also find SV model improves the volatility smile.

並列關鍵字

FFT ； Heston ； SV ； VG ； Ad Hoc BS ； Error Regression

參考文獻

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