Extension of the corrected barrier approximation by Broadie, Glasserman, and Kou

Chapter 8 Discrete Barrier and Lookback Options

“…Of course, as we mentioned, the straightforward result from the central limit theorem, which has error o(1), does not give a good approximation. An approximation based on the results from sequential analysis (see, e.g., Siegmund, 1985 with the error order o(1/ √ m ) is given in Broadie et al (1999), whose proof is simplified in Kou (2003) and Hörfelt (2003). We will review these results in Section 4.…”

“…This is called the change of numeraire argument; for a survey, see Schroder (1999). It is applied to the case of discrete barrier options by Kou (2003) and Hörfelt (2003) independently. However, the methods in Kou (2003) and Hörfelt (2003) lead to slightly different barrier correction formulae.…”

“…It is applied to the case of discrete barrier options by Kou (2003) and Hörfelt (2003) independently. However, the methods in Kou (2003) and Hörfelt (2003) lead to slightly different barrier correction formulae. To illustrate the change of numeraire argument for the discrete barrier options.…”

“…Kou (2003) covered all eight cases with a simpler proof (see also Hörfelt, 2003). The continuity corrections for discrete lookback options are given in Broadie et al (1999).…”

Pricing financial claims contingent upon an underlying asset monitored at discrete times

“…Consequently, for even relatively few dates, numerical evaluation becomes very inefficient. To overcome the mis-pricing, a wide variety of numerical techniques have been proposed in the literature, including recent noteworthy additions [5][6][7][8][9][10][11][12][13][14][15]. This work is a revision of an article by two of the authors [16] in which an exact analytic expression for the down-out option price was obtained as the solution to the Black-Scholes PDE.…”