pith. sign in

arxiv: 2605.19146 · v1 · pith:TJZK7PQOnew · submitted 2026-05-18 · 💱 q-fin.MF · cs.CE

Designing On-Chain Options: Amortizing Perpetual Options

Maxim Bichuch , Zachary Feinstein This is my paper

Pith reviewed 2026-05-20 07:11 UTC · model grok-4.3

classification 💱 q-fin.MF cs.CE
keywords amortizing perpetual optionson-chain optionsDeFitail riskdecentralized clearingperpetual optionsblockchain constraintsendogenous collateralization
0
0 comments X

The pith

Amortizing perpetual options can mutualize tail risk across DeFi protocols without centralized clearing institutions.

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

The paper introduces a design for amortizing perpetual options that fits the operational and adversarial constraints of blockchain environments. Typical options replication requires frequent oracles and liquidations that break under stress, but this approach creates a decentralized market with minimal consistency needs. It positions the contract as a foundational risk primitive supporting endogenous collateralization and explicitly priced de-peg insurance. Readers would care if this enables protocols to share extreme risks mutually rather than depending on central clearing houses.

Core claim

Amortizing perpetual options tailored to blockchain constraints function as a foundational risk primitive for DeFi. They enable a decentralized market framework with minimal consistency requirements. This allows applications including endogenous collateralization and explicitly priced de-peg insurance, demonstrating a layer for mutualizing tail risk across protocols without reliance on centralized clearing institutions.

What carries the argument

The amortizing perpetual option contract, which reduces its notional exposure gradually to align with on-chain constraints and reduce dependence on high-frequency external data.

Load-bearing premise

The assumption that an amortizing perpetual option contract can reliably function as a foundational risk primitive under blockchain operational and adversarial constraints.

What would settle it

A live deployment test during a major market de-peg event to check whether the contracts deliver hedging and insurance without oracle failures or liquidation cascades.

Figures

Figures reproduced from arXiv: 2605.19146 by Maxim Bichuch, Zachary Feinstein.

Figure 1
Figure 1. Figure 1: Visualization of liquidation events due to amortization. The blue line is 30bps/day amor [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
read the original abstract

Financial options are fundamental to traditional markets, enabling strategies ranging from hedging to speculating. Yet, while the Automated Market Maker paradigm has revolutionized decentralized spot markets, no equivalent standard has emerged for on-chain options. Typical designs attempt to replicate centralized exchange mechanics, requiring high-frequency oracles and robust liquidation engines which may fail during stress events. This paper presents a design for amortizing perpetual options tailored to the operational and adversarial constraints of blockchain environments. Leveraging this primitive, we introduce a decentralized market framework with minimal consistency requirements. We demonstrate that this contract functions as a foundational risk primitive for DeFi, enabling applications such as endogenous collateralization and explicitly priced de-peg insurance, thereby showing that this design provides a layer for mutualizing tail risk across protocols without reliance on centralized clearing institutions.

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.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a design for amortizing perpetual options tailored to blockchain constraints, including minimal consistency requirements and avoidance of high-frequency oracles or liquidation engines. It positions this contract as a foundational risk primitive that enables a decentralized market framework for mutualizing tail risk across protocols without centralized clearing institutions, with concrete applications such as endogenous collateralization and explicitly priced de-peg insurance.

Significance. If the design and its claimed properties hold under adversarial conditions, the work would constitute a useful contribution to on-chain derivatives by supplying a risk-management primitive that aligns with blockchain operational realities. The emphasis on minimal consistency requirements and the explicit framing as a mutualization layer are strengths that could support new DeFi constructions; credit is due for focusing on stress-event robustness rather than direct replication of centralized mechanics.

major comments (1)
  1. [Design and Applications sections] The central demonstration that the amortizing perpetual option functions as a risk primitive for mutualizing tail risk (as stated in the abstract and presumably developed in the design and applications sections) requires explicit verification that the amortization schedule prevents the need for external oracles or liquidation engines during tail events; without a concrete derivation or adversarial analysis showing invariance under bounded oracle failures, the load-bearing claim remains unverified.
minor comments (2)
  1. [Design section] Notation for the amortization rate and payoff function should be introduced with a clear equation early in the design section to aid readability.
  2. [Applications] Any numerical examples or parameter choices used to illustrate endogenous collateralization should include sensitivity checks to the amortization period.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment, which identifies a point where additional explicit verification would strengthen the central claim. We have revised the manuscript to incorporate the requested analysis.

read point-by-point responses

  1. Referee: [Design and Applications sections] The central demonstration that the amortizing perpetual option functions as a risk primitive for mutualizing tail risk (as stated in the abstract and presumably developed in the design and applications sections) requires explicit verification that the amortization schedule prevents the need for external oracles or liquidation engines during tail events; without a concrete derivation or adversarial analysis showing invariance under bounded oracle failures, the load-bearing claim remains unverified.

    Authors: We agree that the manuscript would benefit from a more explicit derivation and adversarial analysis to verify the invariance properties. In the revised version, we have added a dedicated subsection to the Design section that derives the amortization schedule's behavior under tail events. The derivation shows that continuous premium amortization maintains collateralization ratios without discrete liquidation thresholds, as the option's notional adjusts proportionally to cumulative deviations in the underlying. We further include an adversarial analysis considering bounded oracle failures (delayed or noisy price feeds within a specified error bound), demonstrating that the mutualization mechanism absorbs the resulting tail risk internally without requiring external oracles or liquidation engines for settlement. This addition directly substantiates the load-bearing claim regarding minimal consistency requirements. revision: yes

Circularity Check

0 steps flagged

Design proposal with no detectable circular derivation chain

full rationale

The paper introduces a tailored contract design for amortizing perpetual options under blockchain constraints, positioning it as a risk primitive for DeFi applications such as endogenous collateralization and priced de-peg insurance. The provided abstract and description contain no equations, fitted parameters, predictions, or self-citations that reduce any claimed result to its own inputs by construction. Claims follow directly from the stated design choices (minimal consistency requirements, avoidance of high-frequency oracles) without self-definitional loops or load-bearing reliance on prior author work. The manuscript is self-contained as a constructive proposal rather than a predictive model, warranting a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the design is described at a high level without explicit mathematical structure or assumptions listed.

pith-pipeline@v0.9.0 · 5654 in / 970 out tokens · 35487 ms · 2026-05-20T07:11:45.208734+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

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

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.

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · 3 internal anchors

  1. [1]

    Adams, H., Zinsmeister, N., Salem, M., Keefer, R., and Robinson, D. (2021). Uniswap v3 core. Uniswap, Tech. Rep

    work page 2021

  2. [2]

    Amini, H., Bichuch, M., and Feinstein, Z. (2025). Decentralized prediction markets and sports books.Mathematical Finance

    work page 2025

  3. [3]

    and Chitra, T

    Angeris, G. and Chitra, T. (2020). Improved price oracles: Constant function market makers. InProceedings of the 2nd ACM Conference on Advances in Financial Technologies, pages 80–91

    work page 2020

  4. [4]

    Angeris, G., Chitra, T., Diamandis, T., Evans, A., and Kulkarni, K. (2023a). The geometry of constant function market makers.arXiv preprint arXiv:2308.08066

    work page arXiv

  5. [5]

    Angeris, G., Evans, A., and Chitra, T. (2023b). Replicating market makers.Digital Finance, 5(2):367–387

    work page

  6. [6]

    and Feinstein, Z

    Bichuch, M. and Feinstein, Z. (2024). Defi arbitrage in hedged liquidity tokens.arXiv preprint arXiv:2409.11339

    work page arXiv 2024

  7. [7]

    and Feinstein, Z

    Bichuch, M. and Feinstein, Z. (2025). Axioms for automated market makers: A mathematical framework in fintech and decentralized finance.Operations Research

    work page 2025

  8. [8]

    and Vandenberghe, L

    Boyd, S. and Vandenberghe, L. (2004).Convex optimization. Cambridge university press

    work page 2004

  9. [9]

    A Utility Framework for Bounded-Loss Market Makers

    Chen, Y. and Pennock, D. M. (2012). A utility framework for bounded-loss market makers. arXiv preprint arXiv:1206.5252

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  10. [10]

    and Caperdoni, C

    Ciurlia, P. and Caperdoni, C. (2009). A note on the pricing of perpetual continuous-installment options.Mathematical Methods in Economics and Finance, 4(1):11–26

    work page 2009

  11. [11]

    O., Chevallier, J., and Sanhaji, B

    Diop, P. O., Chevallier, J., and Sanhaji, B. (2024). Collapse of silicon valley bank and usdc depegging: A machine learning experiment.FinTech, 3(4):569–590

    work page 2024

  12. [12]

    and Zhu, H

    Duffie, D. and Zhu, H. (2011). Does a central clearing counterparty reduce counterparty risk? The Review of Asset Pricing Studies, 1(1):74–95

    work page 2011

  13. [13]

    C., and Clark, J

    Eskandari, S., Salehi, M., Gu, W. C., and Clark, J. (2021). Sok: Oracles from the ground truth to market manipulation. InProceedings of the 3rd ACM Conference on Advances in Financial Technologies, pages 127–141

    work page 2021

  14. [14]

    Fateh Singh, S., Nekriach, V., Michalopoulos, P., Veneris, A., and Klinck, J. (2025). Option contracts in the defi ecosystem: Opportunities, solutions, and technical challenges.International Journal of Network Management, 35(2):e70005

    work page 2025

  15. [15]

    Feinstein, Z. (2026). Amortizing perpetual options.arXiv preprint arXiv:2512.06505. 18

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  16. [16]

    Gogol, K., Velner, Y., Kraner, B., and Tessone, C. (2024). Sok: Liquid staking tokens (lsts) and emerging trends in restaking.arXiv preprint arXiv:2404.00644

    work page arXiv 2024

  17. [17]

    Gudgeon, L., Werner, S., Perez, D., and Knottenbelt, W. J. (2020). Defi protocols for loanable funds: Interest rates, liquidity and market efficiency. InProceedings of the 2nd ACM Conference on Advances in Financial Technologies, pages 92–112

    work page 2020

  18. [18]

    Hanson, R. (2007). Logarithmic market scoring rules for modular combinatorial information aggregation.The Journal of Prediction Markets, 1(1):3–15

    work page 2007

  19. [19]

    Hull, J. C. (2018).Options, Futures, and Other Derivatives. Pearson, 10th edition

    work page 2018

  20. [20]

    Kimura, T. (2009). American continuous-installment options: Valuation and premium decom- position.SIAM Journal on Applied Mathematics, 70(3):803–824

    work page 2009

  21. [21]

    Kimura, T. (2010). Valuing continuous-installment options.European Journal of Operational Research, 201(1):222–230

    work page 2010

  22. [22]

    and Viswanath-Natraj, G

    Kozhan, R. and Viswanath-Natraj, G. (2021). Decentralized stablecoins and collateral risk. WBS Finance Group Research Paper Forthcoming, pages 1–28

    work page 2021

  23. [23]

    and Kristensen, J

    Lambert, G. and Kristensen, J. (2022). Panoptic: the perpetual, oracle-free options protocol. arXiv preprint arXiv:2204.14232

    work page arXiv 2022

  24. [24]

    and Hayes, G

    Leshner, R. and Hayes, G. (2019). Compound: The money market protocol.White Paper, 93

    work page 2019

  25. [25]

    arXiv preprint arXiv:2208.06046 (2022)

    Milionis, J., Moallemi, C. C., Roughgarden, T., and Zhang, A. L. (2022). Automated market making and loss-versus-rebalancing.arXiv preprint arXiv:2208.06046

    work page arXiv 2022

  26. [26]

    Don’t worry about depegs: Introduc- ing depeg cover from nexus mutual.https://nexusmutual.io/blog/ dont-worry-about-depegs-introducing-depeg-cover-from-nexus-mutual

    Nexus Mutual (2025). Don’t worry about depegs: Introduc- ing depeg cover from nexus mutual.https://nexusmutual.io/blog/ dont-worry-about-depegs-introducing-depeg-cover-from-nexus-mutual

    work page 2025

  27. [27]

    Lessons from the crypto winter: DeFi versus CeFi

    OECD (2022). Lessons from the crypto winter: DeFi versus CeFi. Technical report, OECD Business and Finance Policy Papers

    work page 2022

  28. [28]

    Pennella, L., Saggese, P., Pinelli, F., and Galletta, L. (2025). A unified framework and com- parative study of decentralized finance derivatives protocols.arXiv preprint arXiv:2512.19113

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  29. [29]

    Pirrong, C. (2011). The economics of central clearing: theory and practice

    work page 2011

  30. [30]

    Qin, K., Zhou, L., Livshits, B., and Gervais, A. (2021). Attacking the defi ecosystem with flash loans for fun and profit. InInternational conference on financial cryptography and data security, pages 3–32. Springer

    work page 2021

  31. [31]

    C., Kwa´ snicki, M., and Mamageishvili, A

    Schlegel, J. C., Kwa´ snicki, M., and Mamageishvili, A. (2022). Axioms for constant function market makers.arXiv preprint arXiv:2210.00048

    work page arXiv 2022

  32. [32]

    Xu, J., Paruch, K., Cousaert, S., and Feng, Y. (2023). Sok: Decentralized exchanges (dex) with automated market maker (amm) protocols.ACM Computing Surveys, 55(11):1–50

    work page 2023

  33. [33]

    Zargham, M., Shorish, J., and Paruch, K. (2020). From curved bonding to configuration spaces. In2020 IEEE International Conference on Blockchain and Cryptocurrency (ICBC), pages 1–3. IEEE. 19

    work page 2020