G. Alobaidi and R. Mallier, Laplace transforms and the American straddle, Journal of Applied Mathematics, vol.2, issue.3, pp.121-129, 2002.
DOI : 10.1155/S1110757X02110011

G. Barone-adesi and R. E. Whaley, Efficient Analytic Approximation of American Option Values, The Journal of Finance, vol.41, issue.2, pp.301-320, 1987.
DOI : 10.1111/j.1540-6261.1987.tb02569.x

M. Broadie, P. Glasserman, and G. Jain, Enhanced Monte Carlo Estimates for American Option Prices, The Journal of Derivatives, vol.5, issue.1, pp.25-44, 1997.
DOI : 10.3905/jod.1997.407983

P. Carr, R. Jarrow, and R. Myneni, ALTERNATIVE CHARACTERIZATIONS OF AMERICAN PUT OPTIONS, Mathematical Finance, vol.6, issue.2, pp.87-106, 1992.
DOI : 10.1007/BF00250676

J. S. Chaput and L. H. Ederington, Volatility trade design, Journal of Futures Markets, vol.10, issue.3, pp.243-279, 2005.
DOI : 10.1002/fut.20142

C. Chiarella and A. Ziogas, Evaluation of American strangles, Journal of Economic Dynamics and Control, vol.29, issue.1-2, pp.31-62, 2005.
DOI : 10.1016/j.jedc.2003.04.010

J. C. Cox, S. A. Ross, and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, vol.7, issue.3, pp.229-263, 1979.
DOI : 10.1016/0304-405X(79)90015-1

H. U. Gerber and E. S. Shiu, Abstract, ASTIN Bulletin, vol.6, issue.02, pp.195-220, 1994.
DOI : 10.1111/j.1540-6261.1987.tb02569.x

J. Huang, M. G. Subrahmanyam, and G. G. Yu, Pricing and Hedging American Options: A Recursive Integration Method, Review of Financial Studies, vol.9, issue.1, pp.277-300, 1996.
DOI : 10.1093/rfs/9.1.277

J. Hull, Options, Futures and Other Derivatives, 2012.

S. Jacka, Optimal Stopping and the American Put, Mathematical Finance, vol.6, issue.2, pp.1-14, 1991.
DOI : 10.1007/BF00250676

I. Kim, The Analytic Valuation of American Options, Review of Financial Studies, vol.3, issue.4, pp.547-572, 1990.
DOI : 10.1093/rfs/3.4.547

I. I. Kolodner, Free boundary problem for the heat equation with applications to problems of change of phase. I. General method of solution, Communications on Pure and Applied Mathematics, vol.1, issue.1, pp.1-31, 1956.
DOI : 10.1002/cpa.3160090102

P. Linz, Analytical and numerical methods for Volterra equations, 1985.
DOI : 10.1137/1.9781611970852

F. A. Longstaff and E. S. Schwartz, Valuing American Options by Simulation: A Simple Least-Squares Approach, Review of Financial Studies, vol.14, issue.1, pp.113-147, 2001.
DOI : 10.1093/rfs/14.1.113

L. W. Macmillan, An analytical approximation for the American put prices, Advances in Futures and Options Research, vol.1, pp.119-139, 1986.

J. Mckean and H. P. , Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics, Industrial Management Review, vol.6, pp.32-39, 1965.

R. Merton, Theory of Rational Option Pricing, The Bell Journal of Economics and Management Science, vol.4, issue.1, pp.141-183, 1973.
DOI : 10.2307/3003143

F. Moraux, On Perpetual American Strangles, The Journal of Derivatives, vol.16, issue.4, pp.82-97, 2009.
DOI : 10.3905/JOD.2009.16.4.082

URL : https://hal.archives-ouvertes.fr/halshs-00393811

M. Parkinson, Option Pricing: The American Put, The Journal of Business, vol.50, issue.1, pp.21-36, 1977.
DOI : 10.1086/295902

W. H. Press, S. A. Teukolsky, T. Veterling, and B. Flannery, Numerical recipes 3rd edition: The art of scientific computing, 2007.

A. Quarteroni, R. Sacco, and F. Saleri, Numerical mathematics, 2007.
DOI : 10.1007/b98885

N. Taleb, Dynamic hedging: managing vanilla and exotic options, 1997.

P. Wilmott, Paul Wilmott introduces quantitative finance, 2007.