Amortizing Perpetual Options

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.