American Parisian options

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-perpetual case, we have been able to reformulate their price as a function of the exercise frontier. In the perpetual case, closed-form solutions or approximations are obtained by relying on excursion theory. We derive the Laplace transform of the first instant Brownian motion reaches a positive level or, without interruption, spends a given amount of time below zero. We perform a detailed comparison of perpetual standard, barrier and Parisian options.

[1]  M. Yor,et al.  Brownian Excursions and Parisian Barrier Options , 1997, Advances in Applied Probability.

[2]  A. Borodin,et al.  Handbook of Brownian Motion - Facts and Formulae , 1996 .

[3]  A combinatorial approach for pricing Parisian options , 2002 .

[4]  M. Garman.,et al.  Foreign currency option values , 1983 .

[5]  L. Gauthier,et al.  Options Réelles et Options Exotiques, une Approche Probabiliste , 2002 .

[6]  Carole Bernard,et al.  A New Procedure for Pricing Parisian Options , 2005 .

[7]  P. L'Ecuyer,et al.  Variance reduction of Monte Carlo and randomized quasi-Monte Carlo estimators for stochastic volatility models in finance , 1999, WSC'99. 1999 Winter Simulation Conference Proceedings. 'Simulation - A Bridge to the Future' (Cat. No.99CH37038).

[8]  Laurent Gauthier.  Excursions height- and length-related stopping times, and application to finance , 2002, Advances in Applied Probability.

[9]  M. Yor,et al.  Brownian Excursions and Parisian Barrier Options , 1997, Advances in Applied Probability.

[10]  Paul Wilmott,et al.  Pricing Parisan Options , 1999 .

[11]  Ernesto Mordecki,et al.  Optimal stopping for a diffusion with jumps , 1999, Finance Stochastics.

[12]  M. Subrahmanyam,et al.  The Valuation of American Barrier Options Using the Decomposition Technique , 1998 .

[13]  Lixin Wu,et al.  PRICING PARISIAN-STYLE OPTIONS WITH A LATTICE METHOD , 1999 .

[14]  E. Jouini,et al.  Option pricing, interest rates and risk management , 2001 .

[15]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[16]  Mark Schroder,et al.  A parity result for American options , 1998 .

[17]  Paul Wilmott,et al.  Pricing Parisian Options , 1999 .

[19]  J. Detemple.  Série Scientifique Scientific Series American Options: Symmetry Properties , 2022 .

[20]  A New Procedure for Pricing Parisian Options , 2010 .