Reinforcement Learning for Finance

Chapter 7. Dynamic Hedging

Before the advent of Black-Scholes, option markets were sparse and thinly traded. Now they are among the largest and most active security markets. The change is attributed by many to the Black-Scholes model, since it provides a benchmark for valuation and (via the arbitrage argument) a method for replicating or hedging options positions.

Duffie (1998)

Chapter 6 uses deep Q-learning (DQL) to learn how to beat the markets, that is, to learn how to enter long and short positions in a financial instrument in a way that outperforms a benchmark strategy such as, for example, simply going long on the financial instrument. This can be interpreted as trying to prove the efficient market hypothesis (EMH) wrong. Simply speaking, the so-called weak-form EMH postulates that market-observed prices reflect all publicly available information. Timmermann and Granger (2004) provide a modern perspective on and definition of the EMH.

In option pricing—or more generally, derivatives pricing—one generally takes the viewpoint that the market is always right and that one can leverage what is observed in the markets to value derivative instruments whose prices might not be directly observable. In other words, one trusts that markets are efficient and that the EMH holds. This in turn builds the basis for strong arbitrage pricing arguments: two financial instruments have to have the same price if they generate the exact same payoffs in the future. A portfolio of, say, a stock ...