Convergence Rates for Diffusions on Continuous-Time Lattices

22 Pages Posted: 2 Oct 2007


In this paper we introduce a discretization scheme based on a continuous-time Markov chain for the Black-Scholes diffusion process. Our principal aim is to find the optimal convergence rate for the probability density function of the discretized process as the distance between the nodes of the state-space of the Markov chain goes to zero. The main theorem of the paper (theorem 4.1) states that the probability kernel of the discretized process converges at the rate O(h^2) to the probability density function pt(x, y) of the diffusion process. We also show that this convergence is uniform in the state variables x and y and that the proposed discretization scheme converges at a rate which is no faster than O(h^2).

Keywords: Pricing theory, lattice models, convergence estimates

JEL Classification: G13

Suggested Citation

Albanese, Claudio and Mijatovic, Aleksandar, Convergence Rates for Diffusions on Continuous-Time Lattices. Available at SSRN: or

Claudio Albanese (Contact Author)

Global Valuation ( email )

9 Devonshire Sq.
London, London EC2M 4YF
United Kingdom

Aleksandar Mijatovic

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ
United Kingdom


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