This paper examines the valuation of a generalized American-style option known as a game-style call option in an infinite time horizon setting. The specifications of this contract allow the writer to terminate the call option at any point in time for a fixed penalty amount paid directly to the holder. Valuation of a perpetual game-style put optionwas addressed byKyprianou (2004) in a Black-Scho...

Background material on measure-theoretic probability theory and stochastic calculus is provided in order to clarify notation and inform the reader unfamiliar with these concepts. These fields are then employed in exploring two distinct but related approaches to fair option pricing: developing a partial differential equation whose solution, given specified boundary conditions, is the desired fai...

This paper analyzes the performance of two hedging strategies on three different options when trading is limited to take place at discrete times. Specifically, we compare the mean, standard deviation, skewness, and kurtosis of the hedging error resulting from applying a delta hedge and mean square optimal hedge to a European call option, a digital call option, and a down-and-out barrier call op...

Along with the well-known “call-put parity” relation, that makes it possible to express the rational price of a put option in terms of the rational price of a call option, we introduce a “call-put duality” relation. This new concept offers a simple explanation of the relationship between the rational price of a put option and a call option, not only for options of the European type, but also fo...