Speeding up the Euler scheme for killed diffusions

Cetin, Umut and Hok, Julien (2024) Speeding up the Euler scheme for killed diffusions. Finance and Stochastics, 28 (3). 663 - 707. ISSN 0949-2984

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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 E[g(X T)1 {T<ζ}] for a given function g and a deterministic T, where ζ=inf{t≥0:X t∉(ℓ,r)}. It is well known since Gobet (Stoch. Process. Appl. 87:167–197, 2000) 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 discretisations. 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 Çetin (Ann. Appl. Probab. 28:3102–3151, 2018). 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:	© 2024 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HG Finance
JEL classification:	C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C63 - Computational Techniques G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
Date Deposited:	17 Nov 2023 17:30
Last Modified:	20 Sep 2025 02:28
URI:	http://eprintstest.lse.ac.uk/id/eprint/120789

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