April’s seminar was given by Petter Kolm, Clinical Professor and Director of the Mathematics in Finance Master’s program at NYU’s Courant Institute of Mathematical Sciences. His talk was titled “Hedging an options book with reinforcement learning.”
He gave an overview of his joint research with Gordon Ritter, Adjunct Professor at NYU’s Courant Institute of Mathematical Sciences on tackling the problem of how to optimally hedge an options book in practice, where trading decisions are discrete and trading costs can be nonlinear and difficult to model by proposing a model based on the reinforcement learning technique.
Firstly, Professor Kolm gave some background, referring to the seminal work of Black, Scholes & Merton of replicating and hedging an option position, explaining that in practice, portfolio replication is impossible, and an optimal hedging strategy will depend on the desired trade-off between replication error and trading costs.
After a brief literature review of previous work in this area, he then gave an overview of the reinforcement learning technique, detailing the implementation: agent, state space, transaction cost and reward function, which he amounted to automatic hedgers who are prepared to optimise the trade-off cost versus variance.
Professor Kolm then explained how this was applied to a simple example of a European call option with a given strike price and expiry on a non-dividend paying stock, first taking the strike and maturity as fixed and assuming a zero risk-free rate and then extended this for a range of strikes and maturities.
He reported that the implementation was flexible, accurate and promising for real-world applications, pointing out that a key strength of the reinforcement learning approach is not making any assumptions about the form of trading cost and learning the minimum variance hedge subject to the transaction cost function provided, requiring only an environment in which transaction costs and options prices can be simulated accurately.