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

Battle Count: 61

Highly relevant to quantitative trading, particularly for options-based strategies. The framework directly addresses the circular dependency problem in synthetic option data generation, enabling realistic backtesting of short-premium strategies, delta-hedging policies, and deep hedging. The path-conditional Greeks, IV trajectories, and terminal P&L distributions are directly applicable to risk management and strategy evaluation. The cross-ticker validation and earnings-aware calibration address practical concerns for trading around corporate events. The open-source Julia implementation lowers barriers to adoption. The framework's ability to generate out-of-sample tail scenarios is critical for stress testing option portfolios.

The pipeline involves multiple interconnected components: JumpHMM fitting with Student-t copula for multi-asset generation, modified Heston variance process with state-dependent theta, neural surrogate training with joint level-shape optimization, CRR and Leisen-Reimer binomial lattice pricing, finite-difference Greeks computation, and a calibration hierarchy spanning parametric to per-ticker neural representations. The Julia implementation is open-source, but understanding the full pipeline requires knowledge of stochastic volatility modeling, HMMs, copula theory, neural network training, and lattice methods. The calibration on 234,549 observations across 31 tickers and 15 dates adds computational complexity. The temporal holdout and earnings-aware feature engineering add further layers.

The framework is released as an open-source Julia package (https://github.com/varnerlab/heston-implied-volatility-model). The paper provides detailed algorithmic descriptions (Algorithm 1 and 2), explicit parameter values (kappa=2.0, sigma_v=0.5, rho=-0.6, 200/201-step trees), network architectures (4->16->16->1 and 4->8->8->1 MLPs with tanh activations), training schedules (Adam optimizer, step LR schedule, 2000 epochs), and calibration data specifications (31 tickers, 15 dates, 234,549 observations). However, the JumpHMM pretraining details and exact data preprocessing steps for the option ladder are partially described. The use of public Yahoo Finance earnings calendar aids reproducibility.