Drift-Implicit Euler Scheme

Giulia Di Nunno (), Yuliya Mishura () and Anton Yurchenko-Tytarenko ()
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Giulia Di Nunno: University of Oslo, Department of Mathematics
Yuliya Mishura: Taras Shevchenko National University of Kyiv, Department of Probability Theory, Statistics and Actuarial Mathematics
Anton Yurchenko-Tytarenko: Statkraft Energi AS

Chapter 5 in Volterra Volatility Models, 2026, pp 141-175 from Springer

Abstract: Abstract In this chapter, we turn to a more practical question: how to simulate sample paths of sandwiched processes introduced in Chapter 3 . Namely, we suggest the so-called drift-implicit or backward Euler numerical scheme that has an advantage of preserving the bounds of the sandwiched processes, both in one-sided and in two-sided cases. We provide a detailed convergence analysis of the method and support our findings with simulations.

Date: 2026
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DOI: 10.1007/978-3-032-26576-0_5

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