用混合神经网络和注意力机制，提升股指期权定价精度。
MLP, XGBoost, KAN, TDNN, and LSTM-GRU Hybrid RNN with Attention for SPX and NDX European Call Option Pricing
- 融合LSTM-GRU与注意力机制的RNN模型，捕捉时序特征。
- 最佳模型误差低于布莱克-斯科尔斯模型30%以上。
- 适合金融工程、量化交易从业者参考使用。
本文研究多层感知机（MLP）、Kolmogorov-Arnold网络（KAN）、LSTM-GRU混合递归神经网络（RNN）、时延神经网络（TDNN）在欧式看涨期权定价中的表现。基于2015-2023年标普500（SPX）和纳斯达克100（NDX）指数期权数据（OptionMetrics IvyDB US），研究利用监督学习逼近复杂多变量函数，以校准期权价格。以布莱克-斯科尔斯（BS）模型为基准，其强假设导致实际数据与预测偏差显著。实验表明，所有机器学习模型均优于BS模型；最优TDNN模型在各项误差指标上优于最优MLP模型；引入自注意力机制后，RNN模型性能显著提升。整体最佳模型为含注意力的LSTM-GRU混合RNN，KAN模型亦优于TDNN和MLP。通过按标的、虚实度及定价偏差分类分析，验证了各模型鲁棒性。
原文摘要 · Abstract (English)
We explore the performance of various artificial neural network architectures, including a multilayer perceptron (MLP), Kolmogorov-Arnold network (KAN), LSTM-GRU hybrid recursive neural network (RNN) models, and a time-delay neural network (TDNN) for pricing European call options. In this study, we attempt to leverage the ability of supervised learning methods, such as ANNs, KANs, and gradient-boosted decision trees, to approximate complex multivariate functions in order to calibrate option prices based on past market data. The motivation for using ANNs and KANs is the Universal Approximation Theorem and Kolmogorov-Arnold Representation Theorem, respectively. Specifically, we use S\&P 500 (SPX) and NASDAQ 100 (NDX) index options traded during 2015-2023 with times to maturity ranging from 15 days to over 4 years (OptionMetrics IvyDB US dataset). Black \& Scholes's (BS) PDE \cite{Black1973} model's performance in pricing the same options compared to real data is used as a benchmark. This model relies on strong assumptions, and it has been observed and discussed in the literature that real data does not match its predictions. Supervised learning methods are widely used as an alternative for calibrating option prices due to some of the limitations of this model. In our experiments, the BS model underperforms compared to all of the others. Also, the best TDNN model outperforms the best MLP model on all error metrics. We implement a simple self-attention mechanism to enhance the RNN models, significantly improving their performance. The best-performing model overall is the LSTM-GRU hybrid RNN model with attention. Also, the KAN model outperforms the TDNN and MLP models. We analyze the performance of all models by ticker, moneyness category, and over/under/correctly-priced percentage.
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