Deep MVA: Deep Learning for Margin Valuation Adjustment of Callable Products

Abstract

Regulatory initial margin (IM) is being implemented across the financial industry in accordance with BCBS-IOSCO requirements. The regulations target uncleared over-the-counter derivative trading and, among other issues, aim to mitigate counter party credit risk by defining a comprehensive set of rules for initial margin between trading parties. Computing the funding costs of IM, or Margin Valuation Adjustment (MVA), is a major challenge for xVA systems as it requires the future projection of dynamic IM positions. This is particularly challenging for callable products, such as Bermudan swaptions which are complex to price and require path wise exercise tracking in exposure simulations. Brute force simulation of future IM is not feasible due to the excessive computational demands of model calibration and numerical pricing methods. Approximate MVA methods, such as regression techniques, are difficult to design due to the high-dimensionality of the problem. In this paper, we propose a method based on Deep Neural Networks to approximate the Bermudan swaption pricing function and sensitivities. We exploit neural network's high-dimensionality and universal approximation properties to train networks based on prices and sensitivities generated from existing numerical pricing models. The trained neural networks are then used for extremely fast IM simulation where computationally intense numerical methods are replaced by optimized and hardware accelerated neural network inference. We demonstrate that the neural network models deliver exceptional performance, capable of pricing Bermudan Swaption MVAs over 100,000 times faster than traditional approaches while maintaining a high degree of accuracy.

Keywords: Deep Learning, Neural Networks, MVA, xVA, SIMM, Bermudan Swaptions