Randomized Neural Networks for estimation of exposure profiles and Credit Valuation Adjustment (CVA) for American Equity Options

2026-06-23

AI Summary

This study addresses the computational inefficiency of credit valuation adjustment (CVA) and exposure profile estimation for high-dimensional American options within a Monte Carlo framework. To overcome the limitations of the traditional least-squares Monte Carlo (LSM) approach, the authors propose an efficient algorithm based on stochastic feedforward neural networks. The method provides a unified treatment for pricing American options, computing expected exposure, potential future exposure, and unilateral CVA under netting agreements, all within both the Black–Scholes and Heston stochastic volatility models. Numerical experiments demonstrate that, in high-dimensional multi-asset settings, the proposed approach significantly reduces computational cost while maintaining favorable convergence properties, thereby confirming its practicality and scalability for CVA and exposure estimation.

Abstract

This thesis studies the use of randomized neural networks for the estimation of exposure profiles and unilateral CVA of American options within a Monte Carlo framework. The analysis is carried out separately under both Black-Scholes and Heston dynamics, combining American option valuation, expected exposure and potential future exposure estimation, and unilateral CVA calculation with portfolio netting effects. The numerical experiment compares this approach with the classical Least-Squares Monte Carlo (LSM) used as a benchmark in both low-dimensional single-asset and high-dimensional multi-asset scenarios, and also includes a path convergence test and a sensitivity analysis. The results show that the randomized feedforward neural network approach preserves convergence to the LSM benchmark when it is extended from pricing to exposure and CVA estimation, while its main advantage appears in high-dimensional problems, where it scales more efficiently and leads to lower computational cost. These results support the use of randomized neural networks as a useful alternative for exposure and CVA estimation in high-dimensional American-style options.

Problem

• exposure profiles
• Credit Valuation Adjustment
• American options
• high-dimensional
• Monte Carlo

Innovation

• Randomized Neural Networks
• Credit Valuation Adjustment
• American Options
• Monte Carlo Simulation
• High-dimensional Exposure Estimation