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

@article{Cuchiero2020AGA,
  title={A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models},
  author={Christa Cuchiero and Wahid Khosrawi and Josef Teichmann},
  journal={Risks},
  year={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 parametrize the leverage function by a family of feed-forward neural networks and learn their parameters directly from the available market option prices. This should be seen in the context of neural SDEs and (causal) generative adversarial networks: we generate volatility surfaces by specific neural… 

Figures and Tables from this paper

Accuracy of deep learning in calibrating HJM forward curves
TLDR
A new class of volatility operators is introduced which map the square integrable noise into the Filipovi\'{c} space of forward curves, and a deterministic parametrized version of it is specified.
Sig-SDEs model for quantitative finance
TLDR
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.
Solving path dependent PDEs with LSTM networks and path signatures
TLDR
This work identifies the objective function used to learn the PPDE by using martingale representation theorem and can de-bias and provide confidence intervals for then neural network-based algorithm.
A Data-Driven Market Simulator for Small Data Environments
TLDR
A generative model that works reliably in environments where the amount of available training data is notoriously small is presented, and it is shown how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series in such environments where availableTraining data is scarce.
Robust Pricing and Hedging via Neural SDEs
TLDR
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.
Neural SDEs as Infinite-Dimensional GANs
TLDR
This work shows that the current classical approach to fitting SDEs may be approached as a special case of (Wasserstein) GANs, and in doing so the neural and classical regimes may be brought together.
Generative Adversarial Network: Some Analytical Perspectives
TLDR
This subchapter will start from an introduction of GANs from an analytical perspective, then move on the training of GAns via SDE approximations and finally discuss some applications of Gans in computing high dimensional MFGs as well as tackling mathematical finance problems.
Deep ReLU Neural Network Approximation for Stochastic Differential Equations with Jumps
TLDR
It is established that ReLU DNNs can break the curse of dimensionality (CoD for short) for viscosity solutions of linear, possibly degenerate PIDEs corresponding to Markovian jump-diffusion processes.
Consistent Recalibration Models and Deep Calibration
Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to
The Universal Approximation Property
TLDR
A characterization, a representation, a construction method, and an existence result are presented, each of which applies to any universal approximator on most function spaces of practical interest, which improves the known capabilities of the feed-forward architecture.
...
...

References

SHOWING 1-10 OF 84 REFERENCES
Deep calibration of rough stochastic volatility models
TLDR
This work showcases a direct comparison of different potential approaches to the learning stage and presents algorithms that provide a suffcient accuracy for practical use and provides a first neural network-based calibration method for rough volatility models for which calibration can be done on the y.
The calibration of stochastic local-volatility models: An inverse problem perspective
Deep Hedging: Learning to Simulate Equity Option Markets
TLDR
This work demonstrates for the first time that GANs can be successfully applied to the task of generating multivariate financial time series and shows that network-based generators outperform classical methods on a range of benchmark metrics.
Generative Adversarial Nets
We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a
Deep hedging
TLDR
This work presents a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, liquidity constraints or risk limits using modern deep reinforcement machine learning methods and shows that the set of constrained trading strategies used by the algorithm is large enough to ε-approximate any optimal solution.
Calibrating and Pricing with a Stochastic-Local Volatility Model
The constant volatility plain vanilla Black–Scholes model is clearly inadequate to reproduce even plain vanilla option prices observed in the market. Efforts to build a pricing model with modified
A Data-Driven Market Simulator for Small Data Environments
TLDR
A generative model that works reliably in environments where the amount of available training data is notoriously small is presented, and it is shown how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series in such environments where availableTraining data is scarce.
Unbiased deep solvers for parametric PDEs
TLDR
Several deep learning algorithms for approximating families of parametric PDE solutions are developed that are robust with respect to quality of the neural network approximation and consequently can be used as a black-box in case only limited a priori information about the underlying problem is available.
Robust Pricing and Hedging via Neural SDEs
TLDR
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.
Universal features of price formation in financial markets: perspectives from deep learning
Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of market quotes and transactions for US equities, we uncover nonparametric evidence for the
...
...