In this thesis, we study Parisian excursions, which are defined as excursions of Brownian
motion above or below a pre-determined barrier, exceeding a certain time length. Employing …

The Brownian excursion is defined as a standard Brownian motion conditioned on starting
and ending at zero and staying positive in between. The first part of the thesis deals with …

It is well known that valuation of financial derivatives, such as options, is one of the major
topics in quantitative finance research. A Parisian option is a special kind of barrier options …

Research into the direction of specific exotic options–like the Parisians–is often driven by the
analysis of structured products. These products contain features that are similar to exotic …

In this paper, we obtain the density function of the single barrier one-sided Parisian stopping
time. The problem reduces to that of solving a Volterra integral equation of the first kind …

In this paper we obtain a recursive formula for the density of the double-barrier Parisian
stopping time. We present a probabilistic proof of the formula for the first few steps of the …

In this paper, we obtain a recursive formula for the density of the two‐sided Parisian
stopping time. This formula does not require any numerical inversion of Laplace transforms …

We propose a method based on continuous-time Markov chain (CTMC) approximation to
compute the distribution of Parisian stopping times and to price options of Parisian style …

In this article, we describe the various sorts of American Parisian options and propose
valuation formulae. Although there is no closed-form valuation for these products in the non …

In this paper, we study the excursion times of a Brownian motion with drift below and above
a given level by using a simple two-state semi-Markov model. In mathematical finance, these …