scholarly journals AN ANALYTICAL SOLUTION FOR THE TWO-SIDED PARISIAN STOPPING TIME, ITS ASYMPTOTICS, AND THE PRICING OF PARISIAN OPTIONS

2015 ◽  
Vol 27 (2) ◽  
pp. 604-620 ◽  
Author(s):  
Angelos Dassios ◽  
Jia Wei Lim
Keyword(s):  
Analytical Solution ◽  
Stopping Time ◽  
Parisian Options

scholarly journals Recursive formula for the double-barrier Parisian stopping time

2018 ◽  
Vol 55 (1) ◽  
pp. 282-301 ◽  
Author(s):  
Angelos Dassios ◽  
Jia Wei Lim
Keyword(s):  
Stopping Time ◽  
Recursive Formula ◽  
Formal Proof ◽  
Computational Method ◽  
Double Barrier ◽  
Parisian Options ◽  
Probabilistic Proof

Abstract 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 recursion, and then a formal proof using explicit Laplace inversions. These results provide an efficient computational method for pricing double-barrier Parisian options.

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

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