# Non-parametric Pricing and Hedging of Exotic Derivatives

@article{Lyons2019NonparametricPA, title={Non-parametric Pricing and Hedging of Exotic Derivatives}, author={Terry Lyons and Sina Nejad and Imanol Perez Arribas}, journal={Applied Mathematical Finance}, year={2019}, volume={27}, pages={457 - 494} }

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 non-parametrically 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… Expand

#### 10 Citations

Model-free pricing and hedging in discrete time using rough path signatures

- Computer Science
- 2019

It turns out that the only information one needs about the market to dynamically hedge exotic derivatives is the prices of these signature payoffs, which leads to a model-free approach to numerically price and Hedge exotic derivatives from market data - more specifically, from market prices of other exotic derivatives. Expand

Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures

- Mathematics
- Applied Mathematical Finance
- 2019

ABSTRACT We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved… Expand

Sig-SDEs model for quantitative finance

- Computer Science, Economics
- ICAIF
- 2020

This work proposes a novel framework for data-driven model selection by integrating a classical quantitative setup with a generative modelling approach, and develops the Sig-SDE model, which provides a new perspective on neural SDEs and can be calibrated to exotic financial products that depend on the whole trajectory of asset prices. Expand

Optimal Execution of Foreign Securities: A Double-Execution Problem with Signatures and Machine Learning

- Business
- 2020

We employ the expected signature of equity and foreign exchange markets to derive an optimal double-execution trading strategy. The signature of a path of a stochastic process is a sequence of real… Expand

Black-Box Model Risk in Finance

- Economics
- 2021

Machine learning models are increasingly used in a wide variety of financial settings. The difficulty of understanding the inner workings of these systems, combined with their wide applicability, has… Expand

Discrete-time signatures and randomness in reservoir computing

- Medicine, Computer Science
- IEEE transactions on neural networks and learning systems
- 2021

A new explanation of the geometric nature of the reservoir computing (RC) phenomenon is presented and a reservoir system able to approximate any element in the fading memory filters class just by training a different linear readout for each different filter. Expand

Deep Signatures

- Computer Science
- NeurIPS 2019
- 2019

This work proposes a novel approach which combines the advantages of the signature transform with modern deep learning frameworks, and describes how the signaturetransform may be used as a layer anywhere within a neural network. Expand

Deep Signature Transforms

- Computer Science, Mathematics
- NeurIPS
- 2019

This work proposes a novel approach which combines the advantages of the signature transform with modern deep learning frameworks, and describes how the signaturetransform may be used as a layer anywhere within a neural network. Expand

Convolutional Signature for Sequential Data

- Computer Science, Mathematics
- ArXiv
- 2020

A novel neural network based model is proposed which borrows the idea from Convolutional Neural Network to address the problem of exponential growth in the number of features in truncated signature transform. Expand

Numerical method for model-free pricing of exotic derivatives using rough path signatures

- Economics
- 2019

We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by… Expand

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