# Sig-SDEs model for quantitative finance

@article{Arribas2020SigSDEsMF, title={Sig-SDEs model for quantitative finance}, author={Imanol Perez Arribas and Cristopher Salvi and Lukasz Szpruch}, journal={Proceedings of the First ACM International Conference on AI in Finance}, year={2020} }

Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance. In this work, we propose a novel framework for data-driven model selection by integrating a classical quantitative setup with a generative modelling approach. Leveraging the properties of the signature, a well-known path-transform from stochastic analysis that recently emerged as leading machine learning technology for learning time-series data, we develop the Sig-SDE…

## 29 Citations

### Robust Pricing and Hedging via Neural SDEs

- Computer ScienceSSRN Electronic Journal
- 2020

Combining neural networks with risk models based on classical stochastic differential equations (SDEs), the resulting model called neural SDE is an instantiation of generative models and is closely linked with the theory of causal optimal transport.

### Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspective

- Computer ScienceArXiv
- 2022

The algorithm can be seen as a particle method where particles are learning RL-driven agents cooperating towards more general calibration targets, and is able to learn local volatility, as well as path-dependence required in the volatility process to minimize the price of a Bermudan option.

### Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspective

- Computer Science
- 2022

The algorithm can be seen as a particle method à la Guyon et Henry-Labordere where particles, instead of being designed to ensure σ loc ( t, S t ) 2 = E [ σ 2 t | S t ] , are learning RL-driven agents cooperating towards more general calibration targets.

### Distribution Regression for Continuous-Time Processes via the Expected Signature

- Computer Science, MathematicsArXiv
- 2020

A learning framework to infer macroscopic properties of an evolving system from longitudinal trajectories of its components, and recast the complex task of learning a non-linear regression function on probability measures to a simpler functional linear regression on the signature of a single vector-valued path.

### Joint calibration to SPX and VIX options with signature-based models

- Mathematics, Computer Science
- 2023

A stochastic volatility model where the dynamics of the volatility are described by linear functions of the signature of a primary underlying process, which is supposed to be some multidimensional continuous semimartingale is considered.

### Sig-wasserstein GANs for time series generation

- Computer ScienceICAIF
- 2021

The SigWGAN is developed by combining continuous-time stochastic models with the newly proposed signature W1 metric, which allows turning computationally challenging GAN min-max problem into supervised learning while generating high fidelity samples.

### Multi-Asset Spot and Option Market Simulation

- Computer ScienceSSRN Electronic Journal
- 2021

This work addresses the high-dimensionality of market observed call prices through an arbitrage-free autoencoder that approximates efficient low-dimensional representations of the prices while maintaining no static arbitrage in the reconstructed surface.

### Functional Expansions

- Mathematics
- 2022

Path dependence is omnipresent in many disciplines such as engineering, system theory and finance. It reflects the influence of the past on the future, often expressed through functionals. However,…

### Risk-Neutral Market Simulation

- EconomicsSSRN Electronic Journal
- 2022

We develop a risk-neutral spot and equity option market simulator for a single underlying, under which the joint market process is a martingale. We leverage an efficient lowdimensional representation…

### Black-Box Model Risk in Finance

- Computer Science
- 2021

It will be to highlight the various sources of risk that the introduction of machine learning emphasises or de-emphasises, and the possible risk mitigation and management strategies that are available.

## References

SHOWING 1-10 OF 35 REFERENCES

### Robust Pricing and Hedging via Neural SDEs

- Computer ScienceSSRN Electronic Journal
- 2020

Combining neural networks with risk models based on classical stochastic differential equations (SDEs), the resulting model called neural SDE is an instantiation of generative models and is closely linked with the theory of causal optimal transport.

### A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models

- Computer ScienceRisks
- 2020

We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface. To achieve this, we…

### A feature set for streams and an application to high-frequency financial tick data

- Computer ScienceBigDataScience '14
- 2014

The underlying ideas are not limited to financial data streams and have the potential to be applied to many other areas in data mining where the non-commutative nature of streams is of importance, like text mining, bioinformatics or click history.

### Learning from the past, predicting the statistics for the future, learning an evolving system

- Computer Science
- 2013

We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the…

### Di erential equations driven by rough signals

- Mathematics
- 1998

This paper aims to provide a systematic approach to the treatment of differential equations of the type
dyt = Si fi(yt) dxti
where the driving signal xt is a rough path. Such equations are very…

### Non-parametric Pricing and Hedging of Exotic Derivatives

- EconomicsApplied Mathematical Finance
- 2020

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…

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

- Economics, MathematicsApplied 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…

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

- Computer Science, Economics
- 2020

This work employs the expected signature of equity and foreign exchange markets to derive an optimal double-execution trading strategy and employs high-frequency data from Nasdaq and for various currencies to compute the signature of the market.

### Auto-Encoding Variational Bayes

- Computer ScienceICLR
- 2014

A stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case is introduced.