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This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…

Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement…

We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The…

Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem…

Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…

This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…

Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…

We propose a deep neural network framework for computing prices and deltas of American options in high dimensions. The architecture of the framework is a sequence of neural networks, where each network learns the difference of the price…

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…

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…

Hedging a portfolio containing autocallable notes presents unique challenges due to the complex risk profile of these financial instruments. In addition to hedging, pricing these notes, particularly when multiple underlying assets are…

This paper contributes to the existing literature on hedging American options with Deep Reinforcement Learning (DRL). The study first investigates hyperparameter impact on hedging performance, considering learning rates, training episodes,…

This paper explores the application of deep Q-learning to hedging at-the-money options on the S\&P~500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging…

Mathematical modelling is ubiquitous in the financial industry and drives key decision processes. Any given model provides only a crude approximation to reality and the risk of using an inadequate model is hard to detect and quantify. By…

In this paper we show how risk-averse reinforcement learning can be used to hedge options. We apply a state-of-the-art risk-averse algorithm: Trust Region Volatility Optimization (TRVO) to a vanilla option hedging environment, considering…

This paper presents a novel decision-focused framework integrating the physical energy storage model into machine learning pipelines. Motivated by the model predictive control for energy storage, our end-to-end method incorporates the prior…

In this paper, we study the robustness of classical deep hedging strategies under distributional shifts by leveraging the concept of adversarial attacks. We first demonstrate that standard deep hedging models are highly vulnerable to small…

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…

In this paper, we focus on finding the optimal hedging strategy of a credit index option using reinforcement learning. We take a practical approach, where the focus is on realism i.e. discrete time, transaction costs; even testing our…