A Hybrid LSMC–PDE Method for Bermudan Option Pricing under the Gatheral Double Mean-Reverting Model

Battle Count: 71

The paper is primarily a computational/numerical methods contribution to derivatives pricing rather than a trading strategy paper. However, it is highly relevant to quantitative finance practitioners who price and hedge Bermudan/American options under stochastic volatility models. The GDMR model's ability to simultaneously calibrate to SPX and VIX markets makes it practically important. The Hybrid LSMC-PDE method could be used in production pricing engines for exotic derivatives desks. The calibration advantage (computing prices across multiple moneyness levels simultaneously) is directly useful for market-making and risk management workflows.

The implementation requires: (1) correlated Brownian motion simulation with truncated Euler scheme for variance factors, (2) Brownian projection with explicit computation of beta coefficients and residual variance, (3) accumulation of path statistics (Z_n, I_n, B_n) over Euler substeps, (4) FFT-based conditional PDE propagation on a log-price grid, (5) least-squares regression with truncated Gram matrix inverse at each exercise date and asset grid point, (6) backward Bermudan recursion with max operator, and (7) careful handling of the shift convention in Fourier space. The paper provides Algorithm 1 as pseudocode, but the interplay between the variance simulation, Brownian projection, FFT step, and regression requires significant numerical expertise to implement correctly.

The paper provides a complete algorithm (Algorithm 1), detailed parameter set (Table 1), explicit grid settings, basis function specifications, FFT implementation details, and full pricing estimates in Appendix B (Tables B1-B4). The parameter set is taken from Bayer, Gatheral and Karlsmark (2013). However, no code repository is provided, and some implementation details (e.g., exact interpolation scheme, FFT frequency grid) could benefit from further specification.