If the use of infinite time is incorrect or inconsistently applied, then both the upper boundary and the prices for Expirationless Call Options on either dividend or non-dividend paying assets must be less than the asset price (S). Without infinite time, the upper boundary for both expiring options and Expirationless Options must be lower than S. The insertion of historical perpetual warrant prices into this graph shows that empirical evidence supports the rational, logical and intuitive reasons that a more rigorous boundary would not be the flat-lined and inflated boundary that is currently in use throughout the financial industry.


A convex price curve for Expirationless Call Options across a full array of strike prices forms the true upper boundary for all call options. This creates an Expirationless (XPO) Call Option Price Frontier. Free from the fallacy and distortions of infinite time embodied in the BSM False Boundary, the XPO Call Option Price Frontier creates the true arbitrage boundary for all call options. With greater respect for the empirical historical data points, the XPO frontier decreases the size of the price distribution for all expiring call options. Without time decay, XPO Calls become an alternative and less expensive hedging vehicle for creating expiring call options. The cost to manufacture and hedge expiring options will drop. And, the added cost and waste of the False Boundary (i.e., The Infinity Tax), can begin to be eliminated from options customers.



Without markets for Expirationless Options the size of The Infinity Tax and the magnitude of saving from XPOs remains hidden. Savings in hedging costs by using XPOs instead of the False Boundary can be estimated by visualizing different discount levels of the XPO Frontier relative to both the False Upper Boundary and the true and empirical historical data points. We can estimate the historical waste from the BSM Infinity Tax by assuming a percentage savings in hedging cost that would have created lower options premiums and greater price integrity over the past 40 years. Since the adoption of the BSM Regime in 1973, across equities, currencies, interest rate markets and commodities, options customers are estimated to have spent at least $20 trillion in call options premiums. Had the market been allowed to use the correct arbitrage boundaries created by Expiratioless Options, we can estimate the total burden of the BSM Infinity Tax above.