Related papers: Deep self-consistent learning of local volatility

In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…

Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…

Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products…

As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic…

We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual…

Deep learning methods have become a widespread toolbox for pricing and calibration of financial models. While they often provide new directions and research results, their `black box' nature also results in a lack of interpretability. We…

We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of…

The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

While time series momentum is a well-studied phenomenon in finance, common strategies require the explicit definition of both a trend estimator and a position sizing rule. In this paper, we introduce Deep Momentum Networks -- a hybrid…

We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results…

We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…

We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic…

This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm \cite{Leland}. We prove several limit…

This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…

It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is…

This paper presents how to apply the stochastic collocation technique to assets that can not move below a boundary. It shows that the polynomial collocation towards a lognormal distribution does not work well. Then, the potentials issues of…

The quadratic rough Heston model provides a natural way to encode Zumbach effect in the rough volatility paradigm. We apply multi-factor approximation and use deep learning methods to build an efficient calibration procedure for this model.…

The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…

We study the reconstruction of implied volatility surfaces from sparse and noisy option quotes using deep learning models under no-arbitrage constraints. We compare multiple neural architectures, including multilayer perceptrons,…