Amortizing Perpetual Options

Battle Count: 74

The paper introduces a novel derivative instrument (AmPO) that could be traded on exchanges and DeFi platforms. While it does not directly propose trading strategies, it provides the pricing framework, Greeks, and comparative statics necessary for quantitative traders to incorporate AmPOs into portfolios. The positional Vega optimization (Example 3.12) and effective maturity analysis are directly relevant to volatility trading strategies. The fungibility and exchange-tradability aspects make it practically implementable for quantitative trading desks. However, the instrument is novel and not yet available in markets, limiting immediate applicability.

Pricing and Greeks computation are straightforward given the closed-form expressions in Table 1 and Corollaries 3.5-3.6. The key parameters (αC, αP) are simple functions of r, σ, and q. Exercise boundaries have explicit formulas. The main implementation complexity lies in the exchange/DeFi infrastructure to support fungible perpetual options with amortizing notional, including the implicit payment mechanism and notional decay tracking. For a quantitative trading desk, integrating AmPO pricing into existing option pricing libraries would be relatively simple.

The paper provides fully closed-form analytical expressions for AmPO pricing, exercise boundaries, and all Greeks under the Black-Scholes framework. All formulas are explicitly stated in Table 1 and Corollaries 3.5-3.6. Numerical examples (Example 3.8, 3.12) specify all parameters (r=5%, σ=50%, S0=100, K=100). The mathematical proofs are self-contained. No proprietary data or code is required for reproduction.