Comment on 'Pricing double barrier options using Laplace transforms' by Antoon Pelsser

Analysis of quadrature methods for pricing discrete barrier options

“…A mathematically oriented discussion of the barrier option pricing problem is contained in Rich (1994). In a nutshell, there are several approaches to barrier option pricing: (a) the probabilistic method, see Kunitomo and Ikeda (1992); (b) the Laplace Transform technique, see Jamshidian (1997), Geman and Yor (1996), Sbuelz (1999), Pelsser (2000), Fusai (2001); (c) the Black-Scholes PDE, which can be solved using separation of variables, see Hui (1996) and Hui et al (2000) or finite difference schemes, see Boyle and Tian (1998) or Zvan et al (2000); (d) binomial and trinomial trees see Boyle and Lau (1994), Ritchken (1995), Heynen and Kat (1997), Tian (1999); (e) Monte Carlo simulations with various enhancements, see Andersen and Brotherton-Ratcliffe (1996), Baldi et al (1998), Beaglehole et al (1997), Kuan and Webber (2003).…”

An exact analytical solution for discrete barrier options

“…In the case of continuous monitoring, several pricing formulae in the Black-Scholes framework are known, [18,27,35,31,23]. Unfortunately, the discrepancy between option prices under continuous and discrete monitoring can be huge.…”

A Numerical Method for Discrete Single Barrier Option Pricing with Time-Dependent Parameters

“…On the other hand, some other studies Geman and Yor (1996), Hui et al (2000), Kunitomo and Ikeda (1992), Pelsser (2000) and Sü han et al (2013) investigated pricing barrier option under continuous monitoring assumption. There are several drastic discrepancies between option prices under these two mentioned assumptions (see Fusai and Recchioni 2008).…”