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Recursive formula for the double-barrier Parisian stopping time

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

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]
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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 

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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