Specialties: XVA, Credit Valuation Adjustment, CVA, Funding Valuation Adjustment, FVA, Capital Valuation Adjustment, KVA, Margin Valuation Adjustment, MVA, Credit Derivatives, Interest Rate Derivatives, Equity Derivatives, Hybrid Derivatives, Counterparty Credit Risk, ALM, Stochastic Calculus, Applied Mathematics, Numerical Methods, Monte Carlo, C, C++, Excel, VBA, CUDA, GPU, Adjoint Algorithmic Differentiation, AAD, JSON, Python, Machine Learning, Neural Networks, Deep Learning, Reinforcement Learning, Team Management, Basel III, Regulatory Capital, FRTB CVA, Benchmark Rate ReformSpecialties: XVA, Credit Valuation Adjustment, CVA, Funding Valuation Adjustment, FVA, Capital Valuation Adjustment, KVA, Margin Valuation Adjustment, MVA, Credit Derivatives, Interest Rate Derivatives, Equity Derivatives, Hybrid Derivatives, Counterparty Credit Risk, ALM, Stochastic Calculus, Applied Mathematics, Numerical Methods, Monte Carlo, C, C++, Excel, VBA, CUDA, GPU, Adjoint Algorithmic Differentiation, AAD, JSON, Python, Machine Learning, Neural Networks, Deep Learning, Reinforcement Learning, Team Management, Basel III, Regulatory Capital, FRTB CVA, Benchmark Rate Reform
While the needs of XVA and FRTB are currently driving the need for high performance valuations, faster valuations have always been sought after.
The universal approximation theorem of artificial neural networks states that a forward feed network with a single hidden layer can approximate any continuous function, given a finite number of hidden units under mild constraints on the activation functions (see Hornik, 1991; Cybenko, 1989). Deep neural networks are preferred over shallow neural networks, as the later can be shown to require an exponentially larger number of hidden units (Telgarsky, 2016). This paper applies deep learning to train deep artificial neural networks to approximate derivative valuation functions using a basket option as an example. To do so it develops a Monte Carlo …