Efficient simulation of prices for European call options under Heston stochastic-local volatility model: a comparison of methods

Battle Count: 75

The paper is highly relevant for quantitative finance practitioners involved in option pricing, volatility modeling, and risk management. The HSLV model is widely used in industry for calibrating to market implied volatility surfaces. The proposed methods directly address the computational bottleneck of simulating the CIR variance process, which is critical for Monte Carlo pricing of derivatives. The truncated Euler method's efficiency makes it suitable for real-time risk management, while the backward Euler method's accuracy is valuable for model validation and stress testing. However, the paper is primarily a numerical methods contribution rather than a trading strategy paper.

Implementation requires understanding of: (1) Lamperti transformation for CIR SDEs, (2) truncated Euler scheme with explicit truncation mapping, (3) implicit backward Euler with Newton-Raphson iteration, (4) Monte Carlo simulation framework, (5) Dupire local volatility calibration via finite differences, and (6) log-price discretization with correlated Brownian motions. The truncated Euler method is relatively straightforward to implement (explicit scheme), while the backward Euler requires solving a nonlinear equation at each time step. The overall Monte Carlo framework with conditional expectation binning adds moderate complexity.

The paper provides detailed model parameters (gamma=0.95, kappa=1.05, rho=-0.315, theta=0.0855, S0=1, r=0, v0=0.0945, T=5, p=0.25), step sizes, number of paths (10,000), and bins (20). The code was written in Python using Spyder IDE. However, no code repository or dataset is publicly shared. The numerical experiments are reproducible in principle given the stated parameters, but the exact implementation details of the AES method and 2D-COS benchmark are not fully specified.