Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T20:26:47.238Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive formula for the double-barrier Parisian stopping time

Part of: Mathematical finance Markov processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  28 March 2018

Angelos Dassios  and
Jia Wei Lim
Angelos Dassios*
Affiliation:
London School of Economics and Political Science
Jia Wei Lim*
Affiliation:
University of Bristol
*
* Postal address: Department of Statistics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK. Email address: [email protected]
** Postal address: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Brownian excursionParisian stopping timedouble-sided Parisian option

MSC classification

Primary: 65C50: Other computational problems in probability
Secondary: 60J65: Brownian motion 91G60: Numerical methods (including Monte Carlo methods)
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 282 - 301
Copyright
Copyright © Applied Probability Trust 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Anderluh, J. H. M. and van der Weide, J. A. M. (2009). Double-sided Parisian option pricing. Finance Stoch. 13, 205–238. Google Scholar
[2]Broeders, D. and Chen, A. (2010). Pension regulation and the market value of pension liabilities: a contingent claims analysis using Parisian options. J. Banking Finance 34, 1201–1214. CrossRefGoogle Scholar
[3]Chesney, M., Jeanblanc-Pique, M. and Yor, M. (1997). Brownian excursions and Parisian barrier options. Adv. Appl. Prob. 29, 165–184. CrossRefGoogle Scholar
[4]Dassios, A. and Lim, J. W. (2013). Parisian option pricing: a recursive solution for the density of the Parisian stopping time. SIAM J. Financial Math. 4, 599–615. Google Scholar
[5]Dassios, A. and Wu, S. (2011). Double-barrier Parisian options. J. Appl. Prob. 48, 1–20. Google Scholar
[6]Dassios, A. and Wu, S. (2009). On barrier strategy dividends with Parisian implementation delay for classical surplus processes. Insurance Math. Econom. 45, 195–202. Google Scholar
[7]Dassios, A. and Wu, S. (2010). Perturbed Brownian motion and its application to Parisian option pricing. Finance Stoch. 14, 473–494. CrossRefGoogle Scholar
[8]Haber, R. J., Schönbucher, P. J. and Wilmott, P. (1999). Pricing Parisian options. J. Derivatives 6, 71–79. Google Scholar
[9]Labart, C. and Lelong, J. (2009). Pricing double barrier Parisian options using Laplace transforms. Internat. J. Theoret. Appl. Finance 12, 19–44. Google Scholar
[10]Schröder, M. (2003). Brownian excursions and Parisian barrier options: a note. J. Appl. Prob. 40, 855–864. CrossRefGoogle Scholar