Valuation of American Continuous-Installment Options

Abstract

In an American continuous-installment option the premium, instead of being paid up-front, is paid at a certain rate per unit time. At any time at or before maturity date, the holder has the right to terminate payments and either exercise the option or "walk away" from deal. Under the standard Black-Scholes assumptions, we can construct an instantaneous riskless dynamic hedging portfolio and derive a Partial Differential Equation (PDE) for the value of this option. This key result enables us to derive valuation formulas for American continuous-installment options using the well-known integral representation along the early exercise boundary. The finite difference approach to solve the PDE is also examined, and numerical techniques to implement the valuation formulas are presentedOption pricing, Hedging