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基于状态切换收益路径的合成美式期权定价

文章 arXiv papers · 作者: Julia Sun et al.
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总结

该框架解决了合成期权生成中的循环问题：隐含波动率通常根据观察到的期权价格推断，但合成价格又需要以隐含波动率为输入。框架首先使用跳跃隐马尔可夫模型生成多资产股票路径，然后通过改进的Heston方差过程推导隐含波动率路径。方差目标会随状态、到期时间、虚实值程度和市场情绪指标变化。随后使用可重组二叉树格为美式期权定价，并按行权价和到期日分别初始化，旨在无需外部校准即可生成波动率微笑、偏斜和期限结构。

波动率形状函数从参数化基线发展而来，并通过全局共享和行业专属神经替代模型构建。在时间留出测试中，预定公司事件是泛化误差的主要来源；距财报的时间和同行业特征恢复了部分预期信号。作者将该方法应用于真实的近平值合约，并报告生成了路径条件波动率、美式期权希腊值和卖出权利金结果；他们还使用第二种标的考察稳健性。证据仅限于所述采样区间和标的，因此尚不能证明更广泛的表现。

核心观点

  • 跳跃隐马尔可夫模型生成包含状态变化和跨资产尾部依赖的股票路径。
  • 改进的Heston过程根据收益状态和期权特征推导隐含波动率路径。
  • 二叉树格根据生成的波动率曲面为美式期权定价。
  • 神经替代模型估计全局和行业层面的波动率形状。
  • 时间留出测试发现，预定公司事件是预测误差的主要来源之一。

标签

期权股票机器学习衍生品定价波动率
全文
# Synthetic American Option Pricing via Jump-HMM-Driven Heston Implied Volatility


# Synthetic American Option Pricing via Jump-HMM-Driven Heston Implied Volatility









Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a pipeline in which implied volatility emerges as an output of a structural model of equity returns. A Jump Hidden Markov Model produces multi-asset price paths with realistic stylized facts and cross-asset tail dependence; a modified Heston variance process, whose mean-reversion target depends on regime state, days to expiration, moneyness, and a market-mood indicator, converts those paths into implied-volatility paths; and a recombining binomial lattice prices American options from the resulting surface. Initializing variance at its mean-reversion target for each strike-expiration pair lets smile, skew, and term structure emerge without external calibration. We calibrate the shape function through a hierarchy spanning a parametric baseline, a globally shared neural surrogate, and a sector-specific neural surrogate fit to a multi-ticker, multi-sector option ladder. A temporal holdout on a multi-day capture isolated scheduled corporate events as the dominant source of test-time generalization error, and calendar-derived earnings-distance and same-sector peer-coupling features recovered the anticipatory portion of that signal. We then apply the framework as a synthetic-data generator on real near-the-money put and call contracts, forward-simulating price paths, and recovering path-conditional implied volatility, finite-difference American Greeks, and terminal short-premium profit and loss from one coherent simulation, and confirm cross-ticker robustness by re-running on a second underlying from a different sector and volatility regime. The framework is released as an open-source Julia package.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。