Option pricing under sub-mixed fractional Brownian motion based on time-varying implied volatility using intelligent algorithms
Option pricing under sub-mixed fractional Brownian motion based on time-varying implied volatility using intelligent algorithms
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DOI：
10.1007/s00500-023-08647-2
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发表时间：
2023-06
期刊：
影响因子：
4.1
通讯作者：
Jingjun Guo;Weiyi Kang;Yubing Wang
中科院分区：
文献类型：
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作者：
Jingjun Guo;Weiyi Kang;Yubing Wang
在当前复杂的国际地缘政治形势和更加激烈的贸易摩擦背景下，金融资产波动性作为风险分析和期权定价的基础具有重要的研究意义。首先，考虑到金融资产的“长期依赖性”等特征，定价模型可能会变得复杂，导致难以直接计算隐含波动率。建立交易数据和建模值之间的损失函数，发现使用全局最优双重退火算法求解的不同时刻的隐含波动率与广义自回归条件异方差（GARCH）波动率和历史波动率不同。其次，通过深度学习方法，利用先前已知的隐含波动率来预测考虑人们对金融资产未来预期的隐含波动率。实证结果表明，使用长短期记忆（LSTM）和一维卷积神经网络（1D-CNN）方法预测的隐含波动率在期权定价方面表现良好。此外，分形期权定价模型优于传统的布莱克-斯科尔斯（B-S）定价模型。最后，基于累积局部效应（ALE）算法——可以量化分析不同波动率对定价模型的影响——发现利用人工智能算法预测的隐含波动率更符合事实。该研究提倡传统数学模型与新兴智能算法的结合，为投资者和风险管理者提供参考，为金融市场的持续发展做出贡献。
Against the background of the current complex international geopolitical situation and more intense trade frictions, the volatility of financial assets has important research significance as a basis for risk analysis and option pricing. First, considering the characteristics of financial assets—such as “long dependence”—the pricing model can become complicated, making it difficult to calculate the implied volatility directly. Establishing the loss function between the trading data and modeled value, the implied volatility at different moments solved using the global optimal double annealing algorithm was found to differ from the generalized autoregressive conditional heteroskedasticity (GARCH) volatility and historical volatility. Second, the implied volatility considering people’s future expectations of financial assets was predicted using the previously known implied volatility via deep learning methods. The empirical results showed that the implied volatilities predicted using the long short-term memory (LSTM) and one-dimensional convolutional neural network (1D-CNN) methods performed well for option pricing. Moreover, the fractal option-pricing models outperformed the traditional Black–Scholes (B–S) pricing model. Finally, based on the accumulated local effect (ALE) algorithm—which can quantify the impact analysis of different volatilities on pricing models—it was found that the predicted implied volatility using artificial intelligence algorithms was more relevant to the truth. A combination of traditional mathematical models and emerging intelligent algorithms are promoted in this study, providing a reference for investors and risk managers and contributing to the continued development of financial markets.