深度學習在選擇權商品定價之探討-以台灣指數選擇權為例

Deep Learning for Option Pricing Using TAIEX Options

鄭圳宏(Tsun-Hung Cheng)

指導教授 ： 謝承熹

國立臺北商業大學/財經學院/財務金融系研究所/碩士(2019年)

摘要

本研究嘗試將深度學習，應用在選擇權商品的定價，基於Black-Scholes-Merton model (BSM)的基本假設下，本文採用歷史波動度，30日的貨幣市場利率作為無風險利率，並選擇每日成交口數在1000口以上的契約，避免流動性不足造成的極端價格影響模型的訓練成效，並將其以買賣權平價定理(Put-Call-Parity)，置換成賣權(Put)，以利模型的訓練。
訓練結果顯示，對於深度價內的選擇權合約，神經網絡的誤差略高於BSM模型，但對價平或價外的選擇權合約而言，BSM模型較神經網絡的誤差大，根據還原成價格後的神經網絡與市場價格以及BSM與市場價格的MSE與MAE，整體來說，神經網絡模型略優於BSM模型。

關鍵字

選擇權定價 ； 深度學習 ； 人工智慧 ； 神經網絡

並列摘要

This paper explores the pricing of TAIEX put options with deep learning. We first choose the contracts which volume over 1000 lots to avoid the problem of liquidity, then convert call premiums with high strike price to those of put by using the put-call parity. Moreover, we use TAIEX future, historical volatility, and 30-days money market rate as underlying, volatility, and risk-free rate respectively. The inputs of deep learning include the underlying, strike price, volatility, time to maturity, and risk-free rate, as those in the Black-Scholes-Merton Framework.
The results show that the pricing error of deep learning is small than that of Black-Scholes-Merton model for the at-the-money and out-of-the money contracts, based on the criteria of mean square error and mean absolute error. However, the result is opposite for the in-the-money contract. The summary is that the performance of deep learning is slightly better than that of Black-Scholes-Merton model for all contracts.

並列關鍵字

Option Pricing ； Deep Learning ； Artificial Intelligence ； Neural Network

參考文獻

Altman N. S., 1991, “An Introduction to Kernel and Nearest-Neighbor Nonparametric Regression,” The America Statistician. 46(3): 175-185.

Black F. and M. Scholes, 1973, “The valuation of Option and Corporate Liabilities,” Journal of Politiacal Economy, 81, 637-654.

Cortes C. and Vapnik V., 1995, “Support-Vector Networks,” AT&T Bell labs, Holmdel, NJ 07733, USA.

Dechter R., 1986, “Learning while Searching in Constraint-Satisfaction Problems,” University of California, Computer Science Department, Cognitive System Laboratory.

Goodfellow I. J., Pauget-Abadie J. and Merza M. et al, 2014, “Generative Adversarial Networks,” Proceedings of the International Conference on Neural Information Processing Systems , NIPS 2014, pp. 2672–2680.