Deep Hedging

Deep Hedging

Author: Hans Buehler

Publisher:

Published: 2019

Total Pages: 32

ISBN-13:

DOWNLOAD EBOOK

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods.We discuss how standard reinforcement learning methods can be applied to non-linear reward structures, i.e. in our case convex risk measures. As a general contribution to the use of deep learning for stochastic processes, we also show in section 4 that the set of constrained trading strategies used by our algorithm is large enough to ∈-approximate any optimal solution.Our algorithm can be implemented efficiently even in high-dimensional situations using modern machine learning tools. Its structure does not depend on specific market dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available.We illustrate our approach by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard “complete market” solution.This is the "stochastic analysis" version of the paper. A version in machine learning notation is available here "https://ssrn.com/abstract=3355706" https://ssrn.com/abstract=3355706.


Distributional Reinforcement Learning

Distributional Reinforcement Learning

Author: Marc G. Bellemare

Publisher: MIT Press

Published: 2023-05-30

Total Pages: 385

ISBN-13: 0262048019

DOWNLOAD EBOOK

The first comprehensive guide to distributional reinforcement learning, providing a new mathematical formalism for thinking about decisions from a probabilistic perspective. Distributional reinforcement learning is a new mathematical formalism for thinking about decisions. Going beyond the common approach to reinforcement learning and expected values, it focuses on the total reward or return obtained as a consequence of an agent's choices—specifically, how this return behaves from a probabilistic perspective. In this first comprehensive guide to distributional reinforcement learning, Marc G. Bellemare, Will Dabney, and Mark Rowland, who spearheaded development of the field, present its key concepts and review some of its many applications. They demonstrate its power to account for many complex, interesting phenomena that arise from interactions with one's environment. The authors present core ideas from classical reinforcement learning to contextualize distributional topics and include mathematical proofs pertaining to major results discussed in the text. They guide the reader through a series of algorithmic and mathematical developments that, in turn, characterize, compute, estimate, and make decisions on the basis of the random return. Practitioners in disciplines as diverse as finance (risk management), computational neuroscience, computational psychiatry, psychology, macroeconomics, and robotics are already using distributional reinforcement learning, paving the way for its expanding applications in mathematical finance, engineering, and the life sciences. More than a mathematical approach, distributional reinforcement learning represents a new perspective on how intelligent agents make predictions and decisions.


Pricing and Hedging Financial Derivatives with Reinforcement Learning Methods

Pricing and Hedging Financial Derivatives with Reinforcement Learning Methods

Author: Alexandre Carbonneau

Publisher:

Published: 2021

Total Pages: 0

ISBN-13:

DOWNLOAD EBOOK

This thesis studies the problem of pricing and hedging financial derivatives with reinforcement learning. Throughout all four papers, the underlying global hedging problems are solved using the deep hedging algorithm with the representation of global hedging policies as neural networks. The first paper, "Equal Risk Pricing of Derivatives with Deep Hedging'', shows how the deep hedging algorithm can be applied to solve the two underlying global hedging problems of the equal risk pricing framework for the valuation of European financial derivatives. The second paper, "Deep Hedging of Long-Term Financial Derivatives'', studies the problem of global hedging very long-term financial derivatives which are analogous, under some assumptions, to options embedded in guarantees of variable annuities. The third paper, "Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments'', studies derivative prices generated by the equal risk pricing framework for long-term options when shorter-term options are used as hedging instruments. The fourth paper, "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures'', investigates the use of non-translation invariant risk measures within the equal risk pricing framework.


Risk-Averse Reinforcement Learning for Algorithmic Trading

Risk-Averse Reinforcement Learning for Algorithmic Trading

Author: Yun Shen

Publisher:

Published: 2014

Total Pages: 8

ISBN-13:

DOWNLOAD EBOOK

We propose a general framework of risk-averse reinforcement learning for algorithmic trading. Our approach is tested in an experiment based on 1.5 years of millisecond time-scale limit order data from NASDAQ, which contain the data around the 2010 flash crash. The results show that our algorithm outperforms the risk-neutral reinforcement learning algorithm by 1) keeping the trading cost at a substantially low level at the spot when the flash crash happened, and 2) significantly reducing the risk over the whole test period.