Neural network for pricing and universal static hedging of contingent claims

TL;DR

This paper introduces a neural network-based Monte Carlo method for pricing and hedging high-dimensional, path-dependent contingent claims, providing interpretable models and efficient bounds without nested simulations.

Contribution

The paper presents a novel neural network approach that offers interpretable pricing models and duality-based bounds for complex contingent claims without additional simulation costs.

Findings

Effective pricing and hedging of high-dimensional options

Obtaining upper and lower price bounds efficiently

Model interpretability in a financial context

Abstract

We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for interpretability of the model, a feature that is often desirable in the financial context. Specifically, the interpretation leads us to demonstrate that any contingent claim -- possibly high dimensional and path-dependent -- under the Markovian and the no-arbitrage assumptions, can be semi-statically hedged using a portfolio of short maturity options. We show how the method can be used to obtain an upper and lower bound to the true price, where the lower bound is obtained by following a sub-optimal policy, while the upper bound by exploiting the dual formulation. Unlike other duality based upper bounds where one typically has to resort to nested simulation for constructing super-martingales, the martingales in the current approach come at no extra cost, without the need for any sub-simulations. We demonstrate through numerical examples the simplicity and efficiency of the method for both pricing and semi-static hedging of path-dependent options