A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options

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PRICING DISCRETELY MONITORED BARRIER OPTIONS AND DEFAULTABLE BONDS IN LÉVY PROCESS MODELS: A FAST HILBERT TRANSFORM APPROACH (2008, unknown): “…analytical formula for the barrier adjustment to be implemented in the continuous barrier option formula to correct for discrete observations and approximate the discrete barrier option with the continuous one with an appropriately adjusted barrier (see also Kou 2003; Howison and Steinberg 2007).”
Pricing early-exercise and discrete barrier options by fourier-cosine series expansions (2009, methodology): “option price in terms of � t is [ 22 ], finding that γ1 = 1 for the Black-Scholes model.”
Matched Asymptotic Expansions in Financial Engineering (2005, background): “It is clear that the method can be applied in a much wider variety of situations, and although few of these opportunities have yet been exploited, there is corresponding work on American put options close to expiry where both conventional asymptotics and ray methods have been applied (see the recent”