Dynamic fund protection in markets with stochastic volatility and frictions: a double Heston model with transaction costs and its applications

This paper develops a pricing framework for Dynamic Fund Protection (DFP) contracts with lookback features under a double Heston stochastic volatility model with proportional transaction costs. The valuation leads to a multidimensional nonlinear partial differential equation (PDE) involving the underlying price and two variance factors, where a nonlinear term captures the impact of trading frictions. To solve this PDE efficiently, we employ a Random Feature (RF) method (a mesh-free, machine-learning-inspired technique) that approximates the solution in a randomly generated feature space via least-squares minimization of the PDE residual. Numerical experiments demonstrate that the RF solver achieves higher accuracy and faster computation speeds compared to conventional grid-based schemes for the same model. Calibration exercises using equity index and foreign exchange market data show that with transaction costs fixed at representative market levels, calibrating the multifactor volatility dynamics fits implied volatility surfaces significantly better than single-factor benchmarks. We also present novel application case studies, including cross-border digital goods pricing under exchange-rate exposure. The results confirm that our integrated volatility-friction framework offers a robust and computationally tractable approach for pricing and hedging lookback-style protections in realistic market settings.