Paper: arXiv 2512.06505

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a novel, highly creative contract design (Amortizing Perpetual Options) that solves the fungibility issue of continuous-installment options. The mathematical formulation and reduction to perpetual American options are elegant, though empirical backtesting or real market data validation is absent.

Research Flowchart

  flowchart TD
    A["Research Goal: Create fungible continuous-installment options (AmPOs)"] --> B["Design Implicit Payment Scheme<br>(Decay claimable notional via amortization rate)"]
    C["Inputs: Asset Price, Volatility, Interest Rate, Amortization Rate"] --> D["Mathematical Reduction<br>(Map AmPO to Vanilla Perpetual American Option)"]
    B --> D
    D --> E["Derive Analytical Expressions<br>(Exercise boundaries, Option prices, Greeks)"]
    E --> F["Outcomes & Numerical Case Studies<br>(Preserved fungibility & volatility sensitivity tradeoffs)"]