Stochastic volatility models, where the volatility is a stochastic process,
can capture most of the essential stylized facts of implied volatility surfaces
and give more realistic dynamics of the volatility smile or skew. However, they
come with the significant issue that they take too long to calibrate.
Alternative calibration methods based on Deep Learning (DL) techniques have
been recently used to build fast and accurate solutions to the calibration
problem. Huge and Savine developed a Differential Deep Learning (DDL) approach,
where Machine Learning models are trained on samples of not only features and
labels but also differentials of labels to features. The present work aims to
apply the DDL technique to price vanilla European options (i.e. the calibration
instruments), more specifically, puts when the underlying asset follows a
Heston model and then calibrate the model on the trained network. DDL allows
for fast training and accurate pricing. The trained neural network dramatically
reduces Heston calibration's computation time.
In this work, we also introduce different regularisation techniques, and we
apply them notably in the case of the DDL. We compare their performance in
reducing overfitting and improving the generalisation error. The DDL
performance is also compared to the classical DL (without differentiation) one
in the case of Feed-Forward Neural Networks. We show that the DDL outperforms
the DL.

基于深度学习技术的差分深度学习（DDL）方法应用于 Heston 模型下的欧式期权定价与标定，DDL 技术通过快速训练和准确的定价显著减少了 Heston 模型的标定计算时间，并表现优于传统深度学习方法。

应用深度学习校准随机波动率模型

Applying Deep Learning to Calibrate Stochastic Volatility Models

A broad class of stochastic volatility models are defined by systems of
stochastic differential equations. While these models have seen widespread
success in domains such as finance and statistical climatology, they typically
lack an ability to condition on historical data to produce a true posterior
distribution. To address this fundamental limitation, we show how to re-cast a
class of stochastic volatility models as a hierarchical Gaussian process (GP)
model with specialized covariance functions. This GP model retains the
inductive biases of the stochastic volatility model while providing the
posterior predictive distribution given by GP inference. Within this framework,
we take inspiration from well studied domains to introduce a new class of
models, Volt and Magpie, that significantly outperform baselines in stock and
wind speed forecasting, and naturally extend to the multitask setting.

提出了一种将随机波动模型更改为具有特殊协方差函数的分层高斯过程模型的方法，使其可以根据历史数据产生真正的后验分布，同时还将基于大量已研究的领域的启发式设计用于多任务学习，实现了比基线模型更好的股票和风速预测。

利用波动性核和移动平均均值的高斯过程精准预测

Volatility Based Kernels and Moving Average Means for Accurate  Forecasting with Gaussian Processes

A data-driven approach called CaNN (Calibration Neural Network) is proposed
to calibrate financial asset price models using an Artificial Neural Network
(ANN). Determining optimal values of the model parameters is formulated as
training hidden neurons within a machine learning framework, based on available
financial option prices. The framework consists of two parts: a forward pass in
which we train the weights of the ANN off-line, valuing options under many
different asset model parameter settings; and a backward pass, in which we
evaluate the trained ANN-solver on-line, aiming to find the weights of the
neurons in the input layer. The rapid on-line learning of implied volatility by
ANNs, in combination with the use of an adapted parallel global optimization
method, tackles the computation bottleneck and provides a fast and reliable
technique for calibrating model parameters while avoiding, as much as possible,
getting stuck in local minima. Numerical experiments confirm that this
machine-learning framework can be employed to calibrate parameters of
high-dimensional stochastic volatility models efficiently and accurately.

提出了一种数据驱动的方法 CaNN （Calibration Neural Network），用于使用神经网络（ANN）校准金融资产价格模型。该机器学习框架可以有效和准确地校准高维随机波动模型的参数。

一个基于神经网络的金融模型校准框架

A neural network-based framework for financial model calibration

Bayesian inference for stochastic volatility models using MCMC methods highly
depends on actual parameter values in terms of sampling efficiency. While draws
from the posterior utilizing the standard centered parameterization break down
when the volatility of volatility parameter in the latent state equation is
small, non-centered versions of the model show deficiencies for highly
persistent latent variable series. The novel approach of
ancillarity-sufficiency interweaving has recently been shown to aid in
overcoming these issues for a broad class of multilevel models. In this paper,
we demonstrate how such an interweaving strategy can be applied to stochastic
volatility models in order to greatly improve sampling efficiency for all
parameters and throughout the entire parameter range. Moreover, this method of
"combining best of different worlds" allows for inference for parameter
constellations that have previously been infeasible to estimate without the
need to select a particular parameterization beforehand.

本文介绍利用辅助充分交织方法改进随机波动模型的贝叶斯推断方法，有效提高所有参数的采样效率，并可应用于以前难以估计的参数组合。