A Unified Framework and Comparative Study of Decentralized Finance Derivatives Protocols

Fabio Pinelli; Letterio Galletta; Luca Pennella; Pietro Saggese

arxiv: 2512.19113 · v2 · submitted 2025-12-22 · 💻 cs.GT

A Unified Framework and Comparative Study of Decentralized Finance Derivatives Protocols

Luca Pennella , Pietro Saggese , Fabio Pinelli , Letterio Galletta This is my paper

Pith reviewed 2026-05-16 20:52 UTC · model grok-4.3

classification 💻 cs.GT

keywords decentralized financederivativesperpetualsoptionssyntheticsblockchain protocolsmarket simulationsprotocol comparison

0 comments

The pith

A protocol-agnostic framework unifies the structures, market variables, and mechanisms of DeFi derivatives across perpetuals, options, and synthetics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to create a shared formal language for describing how different DeFi derivative instruments are built and how they respond to real market changes. A reader would care because these protocols are expanding quickly yet lack a common way to compare their designs and risks. The framework links three layers: the exact rules of each instrument, the current state of prices and volatility, and the specific ways each protocol enforces its operations. Numerical simulations then track how positions in each category shift when underlying prices move, volatility rises, fees apply, or leverage increases. This produces a structured view that lets observers see common patterns and differences without being locked to any single protocol's code.

Core claim

The paper provides a formal characterization of the main classes of decentralized derivative instruments and develops a protocol-agnostic framework that connects instrument-level specifications, market-state variables, and protocol-level mechanisms. It complements the framework with numerical simulations that evaluate how derivative positions evolve under varying economic conditions, including changes in underlying asset prices, volatility, protocol-specific fees, and leverage.

What carries the argument

The protocol-agnostic framework that links instrument-level specifications, market-state variables, and protocol-level mechanisms.

If this is right

Positions in perpetual contracts adjust continuously with price and leverage while options positions respond mainly to volatility and time decay.
Synthetic instruments introduce additional protocol fees that alter position outcomes differently from the other two classes under the same market shifts.
The framework makes it possible to run side-by-side comparisons of how the same price drop affects exposure across all three instrument types.
Protocol designers can use the connected layers to test new fee structures or leverage limits before deployment.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same layered approach could be extended to map emerging hybrid derivatives that combine features from more than one class.
Risk models for DeFi portfolios could adopt the framework to simulate cross-protocol exposures without needing proprietary code access.
Auditors might apply the simulations to flag when a protocol's fee or leverage settings produce outsized losses under moderate volatility spikes.

Load-bearing premise

That the three chosen categories of perpetuals, options, and synthetics together with the examined protocols stand for the full range of DeFi derivatives and that the simulations match real behavior without live on-chain checks.

What would settle it

Applying the framework to an existing DeFi derivatives protocol outside the studied set and finding that its instrument rules or response to market changes cannot be expressed using the same connections between specifications, states, and mechanisms.

read the original abstract

Decentralized Finance (DeFi) applications introduce novel financial instruments replicating and extending traditional ones through blockchain-based smart contracts. Among these applications, DeFi derivatives protocols enable the creation and trading of decentralized derivative instruments whose value depends on underlying cryptoassets, indices, or other reference variables. Despite their growing significance, however, they remain relatively understudied compared to other DeFi protocols, such as lending protocols and decentralized exchanges. This paper systematically analyzes DeFi derivatives protocols, categorized into perpetuals, options, and synthetics, with the aim of comparing their instrument structures, protocol mechanisms, operational dynamics, and economic agents. We provide a formal characterization of the main classes of decentralized derivative instruments and develop a protocol-agnostic framework that connects instrument-level specifications, market-state variables, and protocol-level mechanisms. We complement the analytical framework with numerical simulations that evaluate how derivative positions evolve under varying economic conditions, including changes in underlying asset prices, volatility, protocol-specific fees, and leverage. Overall, this study provides a structured analytical framework for understanding and comparing the design and functioning of decentralized finance derivatives protocols.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A protocol-agnostic framework for DeFi derivatives that organizes perpetuals, options, and synthetics, with simulations that still need on-chain grounding.

read the letter

The paper's main contribution is a unified way to describe instrument specs, market states, and protocol mechanisms across three categories of DeFi derivatives without tying the model to any single platform. That structure lets them compare how positions respond to price moves, volatility, fees, and leverage in one setup. It fills a gap because most prior work stays inside one protocol or one instrument type. The formal characterization and the side-by-side treatment of economic agents are the parts that actually move the discussion forward. The simulations illustrate the framework in action and show directional differences between the categories, which is helpful for readers who want to see the mechanics play out numerically. The soft spot is the lack of calibration or back-testing against real transaction data, liquidation records, or fee accrual logs from the protocols they study. Without that step the numerical results rest on parametric choices that may not match contract code or liquidity conditions, so any comparative claims about operational dynamics stay provisional. The work is aimed at researchers and protocol designers who need a shared language for DeFi derivatives rather than at traders looking for immediate signals. It is coherent on its own terms and engages the literature without circularity, so it deserves a serious referee who can check the derivations and push for data validation. I would send it to review.

Referee Report

1 major / 2 minor

Summary. The paper claims to systematically analyze DeFi derivatives protocols in the categories of perpetuals, options, and synthetics. It provides a formal characterization of the main classes of decentralized derivative instruments and develops a protocol-agnostic framework connecting instrument-level specifications, market-state variables, and protocol-level mechanisms. This analytical framework is complemented by numerical simulations evaluating how derivative positions evolve under changes in underlying asset prices, volatility, protocol-specific fees, and leverage, with the overall goal of offering a structured approach to understanding and comparing the design and functioning of these protocols.

Significance. If the framework holds, the work would offer a useful structured lens for an understudied area of DeFi, potentially aiding future protocol design and comparative analysis. The protocol-agnostic framing and explicit linkage of instrument specs to market variables and mechanisms represent a constructive step beyond purely descriptive accounts. The numerical simulations add concrete illustrations of position dynamics, though their value depends on the fidelity of the underlying parametric choices.

major comments (1)

[Numerical Simulations] Numerical Simulations section: the comparative conclusions about instrument behavior rest on uncalibrated parametric assumptions for fees, leverage ratios, and liquidation thresholds. No back-testing or calibration against on-chain transaction logs, liquidation events, or fee accrual data from the examined protocols (e.g., GMX, dYdX, Synthetix) is reported, so deviations between modeled and actual contract parameters could render the simulated dynamics unrepresentative of real operational conditions.

minor comments (2)

[Abstract] The abstract and introduction would benefit from an explicit list of the specific protocols chosen within each category (perpetuals, options, synthetics) to clarify the scope of the comparative study.
[Framework section] Notation for market-state variables and protocol mechanisms should be introduced with a single consolidated table early in the framework section to improve readability when the same symbols recur across instrument classes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the sole major comment below, clarifying the purpose of the simulations while proposing targeted revisions to improve transparency without altering the manuscript's core contribution as a protocol-agnostic framework.

read point-by-point responses

Referee: [Numerical Simulations] Numerical Simulations section: the comparative conclusions about instrument behavior rest on uncalibrated parametric assumptions for fees, leverage ratios, and liquidation thresholds. No back-testing or calibration against on-chain transaction logs, liquidation events, or fee accrual data from the examined protocols (e.g., GMX, dYdX, Synthetix) is reported, so deviations between modeled and actual contract parameters could render the simulated dynamics unrepresentative of real operational conditions.

Authors: We agree that the simulations rely on representative rather than empirically calibrated parameters. The numerical examples are designed to illustrate the application of the unified framework across plausible ranges of fees, leverage, and liquidation thresholds drawn from public protocol documentation, not to generate calibrated forecasts or replicate specific historical events. This choice aligns with the paper's primary goal of providing a general, protocol-agnostic analytical lens rather than an empirical study. To address the concern, we will add a new subsection in the Numerical Simulations section that (i) explicitly states the illustrative intent, (ii) tabulates the chosen parameter values alongside their sources in GMX, dYdX, and Synthetix documentation, and (iii) discusses how the framework can be extended with on-chain calibration in future work. We will also revise the abstract and conclusion to temper any comparative language that could be read as empirical claims. revision: partial

Circularity Check

0 steps flagged

No significant circularity: framework built from protocol analysis without self-referential reduction

full rationale

The paper's central contribution is a protocol-agnostic framework that categorizes DeFi derivatives into perpetuals, options, and synthetics, then formally connects instrument specifications, market-state variables, and protocol mechanisms. This is derived by direct analysis of existing protocols rather than by fitting parameters to data and relabeling outputs as predictions. Numerical simulations of position evolution under price, volatility, fee, and leverage changes are presented as evaluations of the framework, not as independent predictions that reduce to the fitted inputs by construction. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatzes smuggled via citation are used to justify the core structure. The derivation remains self-contained and externally falsifiable against on-chain data or alternative categorizations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on standard financial modeling assumptions applied to blockchain instruments; no free parameters or invented entities are evident from the abstract.

axioms (1)

standard math Standard mathematical modeling of financial instruments applies to blockchain-based derivatives.
Invoked to support the formal characterization of instrument classes.

pith-pipeline@v0.9.0 · 5495 in / 1085 out tokens · 23908 ms · 2026-05-16T20:52:43.449784+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

a perpetual futures contract is a tuple: ⟨U, C, L, S, Pentry, Fm⟩ … Monte Carlo framework … geometric Brownian motion dPt=μPt dt+σPt dWt

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Designing On-Chain Options: Amortizing Perpetual Options
q-fin.MF 2026-05 unverdicted novelty 5.0

Introduces amortizing perpetual options as a blockchain-native primitive that supports decentralized risk management including endogenous collateralization and de-peg insurance.

Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages · cited by 1 Pith paper

[1]

(2025, March 29)

Aave Liquidity Protocol. (2025, March 29). Retrieved March 29, 2025, from https://a pp.aave.com/dashboard Ackerer, D., Hugonnier, J., & Jermann, U. (2024).Perpetual futures pricing. National Bureau of Economic Research. Alexander, C., Choi, J., Park, H., & Sohn, S. (2020). Bitmex bitcoin derivatives: Price discovery, informational efficiency, and hedging ...

work page doi:10.1007/978-3-662-63958-0 2025
[2]

Cheng, Z., Deng, J., Wang, T., & Yu, M. (2021). Liquidation, leverage and optimal margin in bitcoin futures markets.Applied Economics,53(47), 5415–5428. Cousaert, S., Xu, J., & Matsui, T. (2022). Sok: Yield aggregators in defi. In2022 ieee international conference on blockchain and cryptocurrency (icbc)(pp. 1– 14). IEEE. De Blasis, R., & Webb, A. (2022). ...

work page 2021
[3]

Do, T., Pham, T.-A., & Tran, T. (2024). Novel perpetual futures market model based on a family of asymptotic power curves. InInternational conference on blockchain(pp. 69–83). Springer. Dune — Crypto Analytics Powered by Community. (2025, March 27). Retrieved March 27, 2025, from https://dune.com/home Eskandari, S., Salehi, M., Gu, W. C., & Clark, J. (202...

work page doi:10.1016/j.jnc 2024
[4]

Xu, J., Paruch, K., Cousaert, S., & Feng, Y. (2023). SoK: Decentralized exchanges (DEX) with automated market maker (AMM) protocols.ACM Comput. Surv., 55(11), 238:1–238:50. Zhang, Z., Xu, C., & Jiang, C. (2024). Practical blockchain-based options contract. IEEE Transactions on Services Computing. 29 A Appendix A.1 Derivatives contracts in traditional fina...

work page 2023
[5]

This serves as a support for read- ers that are not familiar with such concepts

We outline their main properties, how they are traded, and describe their payoff functions. This serves as a support for read- ers that are not familiar with such concepts. A deeper discussion can be found in (Hull & Basu, 2016). Forward contracts are contracts between two parties to buy or sell an asset at a specified future dateT for a price previously ...

work page 2016
[6]

makers” add liquidity (post orders) and “takers

B.1 Notation and Conventions • Pt: underlying mark (or spot) price at timet;P entry: entry mark. • Q: signed exposure inunits of underlyingfor perpetuals (Q >0 long,Q <0 short). • C: posted collateral at entry (assume net of upfront entry fees unless noted). • L: leverage; NV: notional exposure at entry. • S∈ {+1,−1}: position sign (+1 long,−1 short). • F...

work page 2021

[1] [1]

(2025, March 29)

Aave Liquidity Protocol. (2025, March 29). Retrieved March 29, 2025, from https://a pp.aave.com/dashboard Ackerer, D., Hugonnier, J., & Jermann, U. (2024).Perpetual futures pricing. National Bureau of Economic Research. Alexander, C., Choi, J., Park, H., & Sohn, S. (2020). Bitmex bitcoin derivatives: Price discovery, informational efficiency, and hedging ...

work page doi:10.1007/978-3-662-63958-0 2025

[2] [2]

Cheng, Z., Deng, J., Wang, T., & Yu, M. (2021). Liquidation, leverage and optimal margin in bitcoin futures markets.Applied Economics,53(47), 5415–5428. Cousaert, S., Xu, J., & Matsui, T. (2022). Sok: Yield aggregators in defi. In2022 ieee international conference on blockchain and cryptocurrency (icbc)(pp. 1– 14). IEEE. De Blasis, R., & Webb, A. (2022). ...

work page 2021

[3] [3]

Do, T., Pham, T.-A., & Tran, T. (2024). Novel perpetual futures market model based on a family of asymptotic power curves. InInternational conference on blockchain(pp. 69–83). Springer. Dune — Crypto Analytics Powered by Community. (2025, March 27). Retrieved March 27, 2025, from https://dune.com/home Eskandari, S., Salehi, M., Gu, W. C., & Clark, J. (202...

work page doi:10.1016/j.jnc 2024

[4] [4]

Xu, J., Paruch, K., Cousaert, S., & Feng, Y. (2023). SoK: Decentralized exchanges (DEX) with automated market maker (AMM) protocols.ACM Comput. Surv., 55(11), 238:1–238:50. Zhang, Z., Xu, C., & Jiang, C. (2024). Practical blockchain-based options contract. IEEE Transactions on Services Computing. 29 A Appendix A.1 Derivatives contracts in traditional fina...

work page 2023

[5] [5]

This serves as a support for read- ers that are not familiar with such concepts

We outline their main properties, how they are traded, and describe their payoff functions. This serves as a support for read- ers that are not familiar with such concepts. A deeper discussion can be found in (Hull & Basu, 2016). Forward contracts are contracts between two parties to buy or sell an asset at a specified future dateT for a price previously ...

work page 2016

[6] [6]

makers” add liquidity (post orders) and “takers

B.1 Notation and Conventions • Pt: underlying mark (or spot) price at timet;P entry: entry mark. • Q: signed exposure inunits of underlyingfor perpetuals (Q >0 long,Q <0 short). • C: posted collateral at entry (assume net of upfront entry fees unless noted). • L: leverage; NV: notional exposure at entry. • S∈ {+1,−1}: position sign (+1 long,−1 short). • F...

work page 2021