Matched Asymptotic Expansions in Financial Engineering

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Subfields: Finance

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Differential equations and asymptotic solutions for arithmetic Asian options: ‘Black–Scholes formulae’ for Asian rate calls (2008, unknown): “Howison, 2005, [7], contains a highly readable overview and examples of the application of matched asymptotic methods to option pricing problems and, more recently, Howison and co-workers [9, 8] have used the method to obtain quite general continuity corrections for discretely sampled European barri”
A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options (2007, background): “Only if this initial interval is much larger than ∆T (as would be the case for a forward-start barrier option with discrete sampling) do we need to construct a separate expansion for the initial period; apart from remarking that this expansion is straightforward and entails a regular expansion away ”