Amortizing Perpetual Options

2025-12-06

AI Summary

Conventional installment options terminate upon payment default, rendering nominal units non-fungible and incompatible with exchange trading. Method: We propose Amortizing Perpetual Options (AmPOs), which implement implicit installment payments via deterministic decay of the notional principal, thereby eliminating termination risk and ensuring full fungibility across units. Within the Black–Scholes framework, AmPOs are analytically equivalent to perpetual American options with continuous dividend yield, enabling closed-form valuation. Contribution/Results: This work introduces the first fungible, exchange-compatible installment option structure; derives closed-form pricing formulas and explicit optimal exercise boundaries for both call and put AmPOs; and characterizes the systematic impact of the amortization rate on exercise thresholds, effective volatility sensitivity, and Greek measures. Our analysis employs risk-neutral valuation, comparative statics, and continuous-time financial modeling.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Life-Long and Continual Learning

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems

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 a deterministic decay in the claimable notional. This amortization ensures all units evolve identically, preserving fungibility. Under the Black-Scholes framework, AmPO valuation can be reduced to an equivalent vanilla perpetual American option on a dividend-paying asset. In this way, analytical expressions are possible 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.

Problem

• Introduces amortizing perpetual options for exchange-based trading.
• Replaces installment payments with deterministic decay to preserve fungibility.
• Derives analytical valuations and Greeks under the Black-Scholes framework.

Innovation

• Amortizing perpetual options replace installment payments with deterministic decay
• Valuation reduces to vanilla perpetual American options on dividend-paying assets
• Analytical formulas enable Greeks derivation and comparative statics analysis