• Corpus ID: 244117373

Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures

@inproceedings{Buehler2021DeepHL,
  title={Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures},
  author={Hans Buehler and Phillip Murray and Mikko S. Pakkanen and Ben Wood},
  year={2021}
}
We present a machine learning approach for finding minimal equivalent martingale measures for markets simulators of tradable instruments, e.g. for a spot price and options written on the same underlying. We extend our results to markets with frictions, in which case we find “near-martingale measures” under which the prices of hedging instruments are martingales within their bid/ask spread. By removing the drift, we are then able to learn using Deep Hedging a “clean” hedge for an exotic payoff… 

Figures from this paper

Risk-Neutral Market Simulation
We develop a risk-neutral spot and equity option market simulator for a single underlying, under which the joint market process is a martingale. We leverage an efficient lowdimensional representation
Multi-Asset Spot and Option Market Simulation
TLDR
This work addresses the high-dimensionality of market observed call prices through an arbitrage-free autoencoder that approximates efficient low-dimensional representations of the prices while maintaining no static arbitrage in the reconstructed surface.

References

SHOWING 1-10 OF 15 REFERENCES
Deep Hedging
TLDR
This work presents 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 and shows that the set of constrained trading strategies used by the algorithm is large enough to approximate any optimal solution.
Discrete Local Volatility for Large Time Steps (Short Version)
We construct a state-and-time discrete martingale which is calibrated globally to a set of given input option prices which may exhibit arbitrage. We also provide a method to take small steps, fully
Arbitrage-free market models for option prices
In this paper we construct arbitrage-free market models of stochastic volatility type for one stock, one bank account and a finite family of European call options with various strikes and maturities.
Deep Hedging: Learning to Simulate Equity Option Markets
TLDR
This work demonstrates for the first time that GANs can be successfully applied to the task of generating multivariate financial time series and shows that network-based generators outperform classical methods on a range of benchmark metrics.
On a Heath–Jarrow–Morton approach for stock options
TLDR
This paper proves the existence and uniqueness of arbitrage-free models given basic building blocks and provides necessary and sufficient conditions for absence of Arbitrage.
A Data-Driven Market Simulator for Small Data Environments
TLDR
A generative model that works reliably in environments where the amount of available training data is notoriously small is presented, and it is shown how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series in such environments where availableTraining data is scarce.
A market model for stochastic implied volatility
TLDR
The model is able to capture the stochastic movements of a full term structure of implied volatilities and the conditions are derived that have to be satisfied to ensure absence of arbitrage in the model and its numerical implementation is discussed.
The Micro-Price: A High Frequency Estimator of Future Prices
I define the micro-price to be the limit of a sequence of expected mid-prices and provide conditions for this limit to exist. The micro-price is a martingale by construction and can be considered to
The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets
Let χ be a family of stochastic processes on a given filtered probability space (Ω, F, (Ft)t∈T, P) with T⊆R+. Under the assumption that the set Me of equivalent martingale measures for χ is not
AN OLD‐NEW CONCEPT OF CONVEX RISK MEASURES: THE OPTIMIZED CERTAINTY EQUIVALENT
TLDR
It is shown that the negative of the OCE naturally provides a wide family of risk measures that fits the axiomatic formalism of convex risk measures.
...
1
2
...