Market making method reduces trading losses with adaptive pricing
Regret Bounds for Market Making with Persistent Orders
Computer Science and Game TheoryMachine Learning
Summary
This paper looks at how someone who buys and sells assets can set prices in two connected markets without knowing future price changes. The authors present a simple, automatic way to pick prices that limits how much worse the trader does compared to the best fixed or changing prices. Their method works even when market prices might behave unpredictably or adversarially, and it adapts well when prices have certain patterns. This means a trader can make informed pricing decisions without tuning parameters in advance.
What this means in practice
- •For financial traders: Set adaptive bid and ask prices in connected markets to limit losses against unpredictable price movements using a simple automated policy.
- •For automated trading system developers: Design trading algorithms that require no parameter tuning and yield provably low regret when quoting prices with persistent orders over time.
Authors
Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Luigi Foscari, Vinayak Pathak
Abstract
We study adversarial market making with orders that remain active until execution. The maker operates on two markets: a primary market where orders are made and a secondary market where the resulting positions are hedged. In each round, the maker posts a quote on the primary market before observing both primary and secondary market prices. An order executes when the primary price reaches its quote, and the resulting position is immediately offset at the secondary price. When both price sequences are chosen by an adversary over $T$ rounds, we give a simple deterministic policy with regret of order $\log T$ against the best fixed quote (static comparator) and $\sqrt T$ against the best quote for each submission date (dynamic comparator), plus two terms measuring exposure to future primary and secondary prices. These rates remain optimal even when both exposure terms vanish and lower bounds show that the exposure terms are necessary. Our policy naturally extends to simultaneous bids and asks, where we show that static and dynamic regret are both characterized (up to constant factors) by the exposures terms (where the primary price exposure $V_T^{\mathrm{two}}$ now accounts for both bids and asks) and a term of order $\sqrt{V_T^{\mathrm{two}}\log T}$. Our policy is simple, efficient and fully parameterless. We extend this setting by demonstrating how natural assumptions on the price processes lead to improved guarantees without changing the policy.