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Pricing Discrete European Barrier Options Using Lattice Random Walks
Author(s) -
Hörfelt Per
Publication year - 2003
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.t01-1-00178
Subject(s) - random walk , lattice (music) , smoothness , mathematics , brownian motion , valuation of options , initial value problem , mathematical optimization , bellman equation , mathematical economics , statistical physics , econometrics , mathematical analysis , physics , statistics , acoustics
This paper designs a numerical procedure to price discrete European barrier options in Black‐Scholes model. The pricing problem is divided into a series of initial value problems, one for each monitoring time. Each initial value problem is solved by replacing the driving Brownian motion by a lattice random walk. Some results from the theory of Besov spaces show that the convergence rate of lattice methods for initial value problems depends on two factors, namely the smoothness of the initial value (or the value function) and the moments for the increments of the lattice random walk. This fact is used to obtain an efficient method to price discrete European barrier options. Numerical examples and comparisons with other methods are carried out to show that the proposed method yields fast and accurate results.