2025/12/06 by Zachary Feinstein, Feinstein, Zachary · 1 voice · 1 citation
Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #Credit Risk and Financial Regulations #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #q-fin.MF #q-fin.PR
paper · pdf · doi:10.48550/arxiv.2512.06505
openalex publication_date 2025/12/06 · arxiv published 2025/12/06 · openalex created_date 2025/12/10 · arxiv updated 2026/05/15 · openalex updated_date 2026/07/28
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.