CDS Students Propose Models to Solve For the Fundamental Problem of Option Replication
CDS students and affiliates have recently written an article that proposes models to solve the fundamental problem of option replication. “Deep Reinforcement Learning for Option Replication and Hedging” was published by The Journal of Financial Data Science on September 9, 2020.
The paper’s abstract is as follows:
The authors propose models for the solution of the fundamental problem of option replication subject to discrete trading, round lotting, and nonlinear transaction costs using state-of-the-art methods in deep reinforcement learning (DRL), including deep Q-learning, deep Q-learning with Pop-Art, and proximal policy optimization (PPO). Each DRL model is trained to hedge a whole range of strikes, and no retraining is needed when the user changes to another strike within the range. The models are general, allowing the user to plug in any option pricing and simulation library and then train them with no further modifications to hedge arbitrary option portfolios. Through a series of simulations, the authors show that the DRL models learn similar or better strategies as compared to delta hedging. Out of all models, PPO performs the best in terms of profit and loss, training time, and amount of data needed for training.
In finance, replication and hedging of derivatives are fundamental problems. The article makes three essential contributions in seeking a solution. The first is that they develop a system based on the state of the art DRL (deep reinforcement learning) models — “referred to as DQN; DQN with “preserving outputs precisely, while adaptively rescaling targets” (DQN with Pop-Art); and PPO”.1 The system “learns to optimally replicate options with different strikes subject to discrete trading, round lotting, and nonlinear transaction costs.”1
Second, the team highlights that each model “is trained to hedge a whole range of strikes and no retraining is needed when the user changes to another strike within the range.”1 They demonstrate this by “a series of simulations that the DRL models learn similar or better strategies as compared to delta hedging. Out of all models, PPO performs the best in terms of P&L, training time, and amount of data needed for training.”1
Third, the models are general, which allows the user to plug in any option pricing and simulation library and subsequently train them with no further modifications to hedge arbitrary option portfolios.
About the Team:
Jiayi Du is a graduate student at CDS.
Muyang Jin is a graduate student at CDS and a data scientist at SAP.
Petter N. Kolm is a clinical professor and director of the Mathematics in Finance Master’s Program at NYU’s Courant Institute of Mathematical Sciences.
Gordon Ritter is an adjunct professor at the Courant Institute of Mathematical Sciences, NYU Tandon School of Engineering, Baruch College, and Rutgers University and a partner at Ritter Alpha, LP.
Yixuan Wang is a graduate student at CDS and previously was a data scientist at wilde and TMTPost.
Bofei Zhang is a graduate student at CDS and has interned at ByteDance as a Software Engineer and HOLLA Group as a Data Science intern.
To learn more about this project, please visit the article’s Journal of Financial Data Science page.
References
- “Deep Reinforcement Learning for Option Replication and Hedging” by Jiayi Du, Muyang Jin, Petter N. Kolm, Gordon Ritter, Yixuan Wang, and Bofei Zhang
