Speeding up the Euler scheme for killed diffusions

Cetin, Umut and Hok, Julien (2023) Speeding up the Euler scheme for killed diffusions. Finance and Stochastics. ISSN 0949-2984 (In Press)

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Abstract

Let X be a linear diffusion taking values in (ℓ,r) and consider the standard Euler scheme to compute an approximation to [g(XT)1[T<ζ]] for a given function g and a deterministic T, where ζ=inf{t≥0:Xt∉(ℓ,r)}. It is well-known since \cite{GobetKilled} that the presence of killing introduces a loss of accuracy and reduces the weak convergence rate to 1/N‾‾√ with N being the number of discretisatons. We introduce a drift-implicit Euler method to bring the convergence rate back to 1/N, i.e. the optimal rate in the absence of killing, using the theory of recurrent transformations developed in \cite{rectr}. Although the current setup assumes a one-dimensional setting, multidimensional extension is within reach as soon as a systematic treatment of recurrent transformations is available in higher dimensions.

Item Type:	Article
Official URL:	https://link.springer.com/journal/780
Additional Information:	© 2023 Springer
Divisions:	Statistics
Subjects:	H Social Sciences > HG Finance
JEL classification:	C - Mathematical and Quantitative Methods > C0 - General > C00 - General
Date Deposited:	17 Nov 2023 17:30
Last Modified:	08 May 2024 21:24
URI:	http://eprints.lse.ac.uk/id/eprint/120789

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