# Nonparametric pricing and hedging of exotic derivatives

## TL;DR

This paper introduces signature payoffs, a new class of derivatives that enable nonparametric pricing and hedging of exotic derivatives using market data, with demonstrated accuracy and computational efficiency.

## Contribution

It proposes a novel nonparametric approach using signature payoffs to price and hedge exotic derivatives based on existing market prices.

## Key findings

- Accurate pricing and hedging achieved on real and simulated data.
- Method is computationally tractable and scalable.
- Signature payoffs effectively approximate exotic derivatives.

## Abstract

In the spirit of Arrow-Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to nonparametrically price and hedge exotic derivatives in the scenario where one has access to price data for other exotic payoffs. The methodology leads to a computationally tractable and accurate algorithm for pricing and hedging using market prices of a basket of exotic derivatives that has been tested on real and simulated market prices, obtaining good results.