完整市场模型的神经校准

中文摘要 AI 辅助

我们提出一种神经校准方法，可直接从一组给定的期权价格构建可重组二项树。该方法不将连续期权定价函数或局部波动率曲面作为中间对象进行估计，而是使用神经网络对基准格点进行变形，由此得到的离散定价模型保证无套利、完整、易于解释，可直接用于定价及寻找复制交易策略。校准被表述为带惩罚项的优化问题，该问题结合了再定价误差、可容许性惩罚项，以及基于隐含局部波动率的可选空间正则化项。在合成数据与SPX市场数据上的数值实验表明，所提方法的再定价精度高，与近期提出的其他神经校准方法相比具有很强竞争力，且保留了基于格点的定价与对冲的计算优势；特别地，校准后的树可重复用于对允许提前行权的合约定价，甚至可直接用美式期权价格进行校准。

英文摘要

We propose a neural calibration method to construct a recombining binomial tree directly from a set of given option prices. Rather than estimating a continuous option pricing function or a local volatility surface as an intermediate object, a neural network is used to deform a benchmark lattice. This leads to a discrete pricing model which is guaranteed to be arbitrage-free, complete, easy to interpret, and can be used directly for pricing and to find replicating trading strategies. Calibration is formulated as a penalized optimization problem that combines a repricing error with an admissibility penalty, and an optional spatial regularization term based on implied local volatilities. Numerical experiments on synthetic and SPX market data show that the proposed approach yields accurate repricing and is very competitive when compared to recently proposed other neural calibration methods. It preserves the computational advantages of lattice-based valuation and hedging. In particular, the calibrated tree can be reused to price contracts that allow early exercise, and could even be calibrated directly with American option prices.

发表机构

• Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Udine（乌迪内大学经济与统计科学系）
• Faculty of Economics and Business, University of Amsterdam（阿姆斯特丹大学经济商学院）

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