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Analytic Approximation for Prices of American Options, Time-Dependent Settings, Proportional and Discrete Dividends: The Decoupled Volatility Framework

The paper introduces a fast analytic price approximations for American options on log-normal or close to log-normal underlying assets with discrete time-dependent parameters. Two types of dividends considered here are proportional and discrete - strike convention.

The paper considers pricing American options on underlyings with time-dependent (term structured) parameters in a form of analytic approximation. This subject has not been widely covered by openly available references, with a possible exception of [1] and [11]. These publications consider more general underlying assets with time- and state-dependent parameters. Addressing the problem from very different positions, they end up with the price, decomposable into a sum (possibly in infinite) of solutions to simpler problems.

Focused primarily on achieving a potentially extremely high precision in the price, these approaches, due to their nature, could not pay a sufficiend attention to other important practitioners' concerns like stability of Greeks, scalability to larger portfolios, applicability within inverse (calibration) problems as well as purely engineering issues like timing and simplicity of implementation.

Author: Yuriy Shkolnikov