A combinatorial approach for pricing Parisian options

Abstract

This paper provides a discrete time algorithm, in the framework of the Cox-Ross-Rubinstein analysis (1979), to evaluate both Parisian options with a flat barrier and Parisian options with an exponential boundary. The algorithm is based on a combinatorial tool for counting the number of paths of a particle performing a random walk, that remains beyond a barrier constantly for a period strictly smaller than a pre-specified time interval. As a result, a binomial evaluation model is derived that is very easy to implement and that produces highly accurate prices. (2000): 05A10, 91B28 Mathematics Subject Classification

An improved combinatorial approach for pricing Parisian options

“…If the barrier must be breached for a pre-specified length of time, the so-called window period for it to take effect, we then have a Parisian option. See Costabile (2002b) for more literature on Parisian options. Here we review some tree-like approaches to pricing Parisian options.…”

“…Section 2 reviews the combinatorial approach for pricing Parisian options by Costabile (2002b). Section 3 introduces our improved algorithm.…”

“…Kwok and Lau (2001) used the forward shooting grid approach. Costabile (2002b) proposed a combinatorial approach with a time complexity of O n 3 . This paper will improve and extend Costabile's algorithm.…”

Pension regulation and the market value of pension liabilities: A contingent claims analysis using Parisian options

“…Delayed closure procedure. In the literature, various approaches are applied to valuing standard Parisian derivatives, such as Monte-Carlo algorithms (Andersen and Brotherton-Ratcliffe (1996)), binomial or trinomial trees (Avellaneda and Wu (1999); Costabile (2002)), partial differential equations (Haber et. al (2002)), finite-element methods (Stokes and Zhu (1999)) or the original inverse Laplace transform technique (initiated by Chesney et al (1997)).…”

Default risk, bankruptcy procedures and the market value of life insurance liabilities

“…Various approaches are applied to valuing standard Parisian products, such as MonteCarlo algorithms (Andersen and Brotherton-Ratcliffe (1996)), binomial or trinomial trees (Avellaneda and Wu (1999), Costabile (2002)), PDEs (Haber et. al (2002)), finite-element methods (Stokes and Zhu (1999)) or the implied barrier concept (Anderluh and van der Weide (2004)).…”