Learning To Trade
Deep HedgingHans Buehler
Learning to Tradeat the AI/ML Summit at QuantMinds in Barcelona, December 2021; of the Bachelier Conference talk June 2022; and the TU Munich material summer 2022.
The ambition of learning to trade is moving
away from classic model-driven pricing and
hedging methodologies and focus instead on real life performance
of our now data-driven models, under transaction cost and trading
restrictions across time. Our methods do not rely on greeks as primary
risk management tool anymore. Putting ML as a tool aside,
intuitively we try ask
The core of our approach is not new - indeed, there is a wide range of literature on how to move beyond the classic assumption of full replication of a derivative and assess the impact of transaction cost and market frictions; here are some thoughts from my two university supervisors. What is new is that we now have the computational tools to being able to solve such problems efficiently.
Essentially, we propose to solve the original hedging problem, using data and AI. In somce cases, it is sufficient to use rather straight forward 'regression' methods, which we call Statistical Hedging. For products which have no observable market prices, or for portfolios with path dependence, we have developed Deep Hedging. Vanilla Deep Hedging requires simulators of the market (e.g. stock and implied volatility) to generate sufficient synthetic data. Such simulators are once again built with modern quanti finance and AI methods
Market data, simulated or played back, will naively pick up the historic drifts in our spot and option market. However, the drift is well-known to be subject to model uncertainty. Unless this is explicitly modelled (e.g model alpha), we propose to increase robustnness by finding a close martingale measure, and then find an optimal hedging strategy using Deep Hedging.
Our approach is rather generic and applicable to most commonly traded derivatives. It is not limited to equities markets.
The original Deep Hedging approach uses essentially a Monte Carlo "periodic policy search" algorithm. That means that we have to re-train our agent networks any time our portfolio or the market changes sufficiently. The working paper Deep Bellman Hedging addresses this by expanding our a patent application beyond the entropy, and, importantly, by providing an implementable and realistic representation for "any" portfolio of derivatives. The latter is one of the most challenging aspects of dynamic programming for Deep Hedging.
Lecture NotesThe following lecture notes summarize the overall Learning to Trade topic:
GIT hubGit Hub repositiory for Deep Hedging
Podcasts and presentations
Publicly available Presentations
|Dr. Hans Buehler (connect via linkedin or have a look at my website)