用跳跃隐马尔可夫模型生成真实期权价格,突破传统数据依赖瓶颈。
Synthetic American Option Pricing via Jump-HMM-Driven Heston Implied Volatility

- 基于跳变隐马尔可夫模型生成多资产价格路径,捕捉尾部相关性。
- 通过状态依赖的随机波动率过程自然生成波动率微笑、偏斜与期限结构。
- 可生成带希腊值和损益的合成数据,适合金融风险建模与机器学习训练。
生成真实合成期权价格需以隐含波动率为输入,但隐含波动率本身由观测期权价格推导而来,形成循环依赖,限制了机器学习与风险分析中的合成数据应用。本文提出一种新流程,使隐含波动率成为股权收益结构模型的输出。首先,跳跃隐马尔可夫模型生成具有真实统计特征及跨资产尾部依赖的多资产价格路径;其次,改进的赫斯顿波动率过程根据状态、到期日、实值程度与市场情绪指标动态调整均值回归目标,将路径转化为隐含波动率路径;最后,使用可重组二叉树对美式期权定价。针对每个行权价-到期组合,以均值回归目标初始化波动率,无需外部校准即可自然生成波动率微笑、偏斜与期限结构。通过分层校准策略(参数基线、全局共享神经代理、行业特异性神经代理)拟合形状函数。在多日数据上进行时间留出测试,发现企业事件是主要泛化误差来源,引入基于日历的财报距离与同行业关联特征后,恢复了预期信号。将框架应用于真实近价看涨/看跌合约,实现价格路径前向模拟,并同步获取路径条件隐含波动率、有限差分美式希腊值及到期时的短期溢价损益。在另一不同行业、不同波动率环境的标的上复现验证了跨标的鲁棒性。代码以开源 Julia 包形式发布。
原文摘要 · Abstract (English)
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.
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