IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2512.06505.html

Amortizing Perpetual Options

Author

Listed:
  • Zachary Feinstein

Abstract

In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying fungibility across units of notional. AmPOs replace explicit installment payments and the need for lapsing logic with an implicit payment scheme via the decay of the claimable notional. This amortization ensures all units evolve identically, preserving fungibility. We demonstrate that AmPO valuation can be reduced to an equivalent vanilla perpetual American option on a dividend-paying asset. This enables analytical expressions for the exercise boundaries and risk-neutral valuations for calls and puts. These formulas and relations allow us to derive the Greeks and study comparative statics with respect to the amortization rate. Illustrative numerical case studies demonstrate how the amortization rate shapes option behavior and reveal the resulting tradeoffs in the effective volatility sensitivity.

Suggested Citation

  • Zachary Feinstein, 2025. "Amortizing Perpetual Options," Papers 2512.06505, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2512.06505
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2512.06505
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shiller, Robert J, 1993. "Measuring Asset Values for Cash Settlement in Derivative Markets: Hedonic Repeated Measures Indices and Perpetual Futures," Journal of Finance, American Finance Association, vol. 48(3), pages 911-931, July.
    2. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden & Anthony Lee Zhang, 2022. "Automated Market Making and Loss-Versus-Rebalancing," Papers 2208.06046, arXiv.org, revised May 2024.
    3. Srisht Fateh Singh & Reina Ke Xin Li & Samuel Gaskin & Yuntao Wu & Jeffrey Klinck & Panagiotis Michalopoulos & Zissis Poulos & Andreas Veneris, 2025. "Modeling Loss-Versus-Rebalancing in Automated Market Makers via Continuous-Installment Options," Papers 2508.02971, arXiv.org.
    4. Ben-Ameur, Hatem & Breton, Michele & Francois, Pascal, 2006. "A dynamic programming approach to price installment options," European Journal of Operational Research, Elsevier, vol. 169(2), pages 667-676, March.
    5. Detemple, Jérôme & Laminou Abdou, Souleymane & Moraux, Franck, 2020. "American step options," European Journal of Operational Research, Elsevier, vol. 282(1), pages 363-385.
    6. Mark H.A. Davis & Walter Schachermayer & Robert G. Tompkins, 2002. "Installment Options and Static Hedging," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 3(2), pages 46-52, January.
    7. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
    8. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    9. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 143-165, February.
    10. Guillaume Lambert & Jesper Kristensen, 2022. "Panoptic: the perpetual, oracle-free options protocol," Papers 2204.14232, arXiv.org, revised Jun 2023.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joanna Goard & Mohammed AbaOud, 2022. "Pricing European and American Installment Options," Mathematics, MDPI, vol. 10(19), pages 1-27, September.
    2. Deng Guohe & Xue Guangming, 2016. "Valuation of American Continuous-Installment Options Under the Constant Elasticity of Variance Model," Journal of Systems Science and Information, De Gruyter, vol. 4(2), pages 149-168, April.
    3. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
    4. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing European continuous-installment strangle options," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    5. Liu, Yu-hong & Jiang, I-Ming & Hsu, Wei-tze, 2018. "Compound option pricing under a double exponential Jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 43(C), pages 30-53.
    6. Corinne Powers, 2024. "A Tick-by-Tick Solution for Concentrated Liquidity Provisioning," Papers 2405.18728, arXiv.org.
    7. Lily Y. Liu, 2017. "Estimating Loss Given Default from CDS under Weak Identification," Supervisory Research and Analysis Working Papers RPA 17-1, Federal Reserve Bank of Boston.
    8. Pesaran, M. Hashem & Schuermann, Til & Treutler, Bjorn-Jakob & Weiner, Scott M., 2006. "Macroeconomic Dynamics and Credit Risk: A Global Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(5), pages 1211-1261, August.
    9. Gong, Pu & Zou, Dong & Wang, Jiayue, 2018. "Pricing and simulation for real estate index options: Radial basis point interpolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 177-188.
    10. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1422-1460, October.
    11. A. Itkin & V. Shcherbakov & A. Veygman, 2019. "New Model For Pricing Quanto Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-37, May.
    12. Marco Matsumara & Ajax R.B. Moreira, 2005. "Can Macroeconomic Variables Account for the Term Structure of Sovereign Spreads? Studying the Brazilian Case," Discussion Papers 1106, Instituto de Pesquisa Econômica Aplicada - IPEA.
    13. Giampaolo Gabbi & Andrea Sironi, 2005. "Which factors affect corporate bonds pricing? Empirical evidence from eurobonds primary market spreads," The European Journal of Finance, Taylor & Francis Journals, vol. 11(1), pages 59-74.
    14. Benbouzid, Nadia & Leonida, Leone & Mallick, Sushanta K., 2018. "The non-monotonic impact of bank size on their default swap spreads: Cross-country evidence," International Review of Financial Analysis, Elsevier, vol. 55(C), pages 226-240.
    15. Allan Beltrán & David Maddison & Robert J. R. Elliott, 2018. "Assessing the Economic Benefits of Flood Defenses: A Repeat‐Sales Approach," Risk Analysis, John Wiley & Sons, vol. 38(11), pages 2340-2367, November.
    16. Diaz Weigel, Diana & Gemmill, Gordon, 2006. "What drives credit risk in emerging markets? The roles of country fundamentals and market co-movements," Journal of International Money and Finance, Elsevier, vol. 25(3), pages 476-502, April.
    17. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    18. Hong-Ming Yin & Jin Liang & Yuan Wu, 2018. "On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate," JRFM, MDPI, vol. 11(4), pages 1-12, December.
    19. Rafal M. Wojakowski & M. Shahid Ebrahim & Aziz Jaafar & Murizah Osman Salleh, 2019. "Can Loan Valuation Adjustment (LVA) approach immunize collateralized debt from defaults?," Financial Markets, Institutions & Instruments, John Wiley & Sons, vol. 28(2), pages 141-158, May.
    20. Alexey Litvinenko, 2023. "A Comparative Analysis of Altman's Z-Score and T. Jury's Cash-Based Credit Risk Models with The Application to The Production Company and The Data for The Years 2016-2022," Accounting and Management Information Systems, Faculty of Accounting and Management Information Systems, The Bucharest University of Economic Studies, vol. 22(3), pages 518-553, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2512.06505. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.