Neural Network Construction Methods for Derivatives Modellings

Investment Banks and Market Makers make heavy use of pricing functions for derivatives.

For different applications, there may be a different tradeoff between

Towards this, neural networks can be applied in several ways, not limited on:

1. Pre-train a neural network offline on prices / greeks. This can be done for any vanilla Europeans, or even weakly path-dependent payoffs (barriers, asians) but likely not for more complex payoff structures (e.g. Americans), given the need for one neural net per payoff contract. (For the American case, a neural network is needed for each exercise structure)
2. Solve a pricing problem on-the-fly, at a significantly quicker speed (and sufficient accuracy) than existing methods.

Given unlimited compute power, we could brute-force. However, is there a way

• Neural Network Theory: Neural Network Theory: Universal Approximation, Activation Functions

Volatility / Market Models and Payoffs

Interest Rate Models

• Interest Rate Models

Interest Rate Model Calibration

• Andres Hernandez, Model Calibration with Neural Networks (2016) examines calibrating Hull-White with a neural network

Credit Risk Modelling

• Gerardo Manzo, Xiao Qiao, Deep Learning Credit Risk Modeling (2021) explores calibrating credit risk models to Heston and other vol models with Deep Learning, and has code available at: https://github.com/gmanzog/DeepLearningCreditRiskModeling

Applications

Risk Modelling

• Risk Modelling

XVA

• ALESSANDRO GNOATTO, ATHENA PICARELLI, AND CHRISTOPH REISINGER, DEEP XVA SOLVER – A NEURAL NETWORK BASED COUNTERPARTY CREDIT RISK MANAGEMENT FRAMEWORK (2021)

Alternative Methods

Aside from using neural networks

• Gaussian Processes: Using Gaussian Process Regression for derivatives pricing and risks
• Tensor Methods: Using tensor methods.

TOdo

• Abstract
• PDE, Longstaff Schwartz
• Univeral Approximation, NTK