Related papers: Fast Deep Hedging with Second-Order Optimization
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under…
Deep hedging trains neural networks to manage derivative risk under market frictions, but produces hedge ratios with no measure of model confidence -- a significant barrier to deployment. We introduce uncertainty quantification to the deep…
A key challenge that threatens the widespread use of neural networks in safety-critical applications is their vulnerability to adversarial attacks. In this paper, we study the second-order behavior of continuously differentiable deep neural…
We consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him…
In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which…
In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
Techniques from deep learning play a more and more important role for the important task of calibration of financial models. The pioneering paper by Hernandez [Risk, 2017] was a catalyst for resurfacing interest in research in this area. In…
We present a novel second-order trajectory optimization algorithm based on Stein Variational Newton's Method and Maximum Entropy Differential Dynamic Programming. The proposed algorithm, called Stein Variational Differential Dynamic…
In recent decades, companies have frequently adopted share repurchase programs to return capital to shareholders or for other strategic purposes, instructing investment banks to rapidly buy back shares on their behalf. When the executing…
In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A…
First-order optimization methods remain the standard for training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by preconditioning the stochastic gradient with a diagonal matrix. Despite the…
Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained…
In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simplest algorithm for the problem of prediction with expert…
This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study…
Deep neural policies have unlocked agile flight for quadcopters, adaptive grasping for manipulators, and reliable navigation for ground robots, yet their millions of weights conflict with the tight memory and real-time constraints of…
We present a reinforcement-learning (RL) framework for dynamic hedging of equity index option exposures under realistic transaction costs and position limits. We hedge a normalized option-implied equity exposure (one unit of underlying…