Related papers: Fast Deep Hedging with Second-Order Optimization
Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned optimizers may similarly outperform current hand-designed optimizers, especially…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…
In the context of the optimization of Deep Neural Networks, we propose to rescale the learning rate using a new technique of automatic differentiation. This technique relies on the computation of the {\em curvature}, a second order…
Using techniques from deep learning (cf. [B\"uh+19]), we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in the context of partial hedging by [FL00]. Not only does…
We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…
This paper shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The paper illustrates the approach by showing the difference between using delta hedging and…
This paper explores second-order optimization methods in Federated Learning (FL), addressing the critical challenges of slow convergence and the excessive communication rounds required to achieve optimal performance from the global model.…
Distributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some…
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.…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
Policy gradient methods are a powerful family of reinforcement learning algorithms for continuous control that optimize a policy directly. However, standard first-order methods often converge slowly. Second-order methods can accelerate…
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…
Second-order optimizers are thought to hold the potential to speed up neural network training, but due to the enormous size of the curvature matrix, they typically require approximations to be computationally tractable. The most successful…
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…
We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$.…
In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…
Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…
While the superior performance of second-order optimization methods such as Newton's method is well known, they are hardly used in practice for deep learning because neither assembling the Hessian matrix nor calculating its inverse is…
Training deep neural networks consumes increasing computational resource shares in many compute centers. Often, a brute force approach to obtain hyperparameter values is employed. Our goal is (1) to enhance this by enabling second-order…