Lifted Heston Model: Efficient Monte Carlo Simulation with Large Time Steps

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Highly relevant for quantitative trading desks dealing with volatility derivatives (VIX options, variance swaps). The method enables efficient Monte Carlo pricing with large time steps, significantly reducing computational cost for real-time pricing and risk management. The lifted Heston model captures rough volatility features important for accurate implied volatility surface calibration. Directly applicable to pricing and hedging exotic volatility products.

Moderate to high complexity. Requires: (1) construction and eigen-decomposition of N×N matrices, (2) solving N-dimensional ODE systems for the deterministic component ξ, (3) computing matrix exponentials, (4) sampling from inverse Gaussian distributions, (5) implementing the constraint feasibility check and constrained optimization, (6) handling the state process updates for N auxiliary processes. The algorithm is well-structured but involves significant linear algebra operations that scale with N.

The paper provides a complete algorithm (Algorithm 1), detailed parameter sets for numerical experiments, analytical derivations of all required quantities, and mentions an accompanying Python implementation on GitHub. However, the specific GitHub URL is not provided in the text. The method requires solving N-dimensional linear systems and ODEs, which are well-defined but computationally involved.