Replicating market makers

Guillermo Angeris (), Alex Evans () and Tarun Chitra ()
Additional contact information
Guillermo Angeris: Bain Capital Crypto
Alex Evans: Bain Capital Crypto
Tarun Chitra: Gauntlet Networks

Digital Finance, 2023, vol. 5, issue 2, No 4, 367-387

Abstract: Abstract We present a method for constructing constant function market makers (CFMMs) whose portfolio value functions match a desired payoff. More specifically, we show that the space of concave, nonnegative, nondecreasing, 1-homogeneous payoff functions and the space of convex CFMMs are equivalent; in other words, every CFMM has a concave, nonnegative, nondecreasing, 1-homogeneous payoff function, and every payoff function with these properties has a corresponding convex CFMM. We demonstrate a simple method for recovering a CFMM trading function that produces this desired payoff. This method uses only basic tools from convex analysis and is intimately related to Fenchel conjugacy. We demonstrate our result by constructing trading functions corresponding to basic payoffs, as well as standard financial derivatives, such as options and swaps.

Keywords: Constant function market makers; Decentralized finance; Convex optimization; Fenchel conjugacy (search for similar items in EconPapers)
JEL-codes: C65 D47 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s42521-023-00082-0

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