472
Views
7
CrossRef citations to date
0
Altmetric
Research Papers

American-type basket option pricing: a simple two-dimensional partial differential equation

&
Pages 1689-1704 | Received 13 Apr 2018, Accepted 22 Feb 2019, Published online: 12 Apr 2019

References

  • Ahmad, R. and Asif, K., Numerical and Computational Methods for Derivative Pricing, 2006 (John Wiley & Sons: Chichester).
  • Björk, T., Arbitrage Theory in Continuous Time, 1998 (Oxford University Press: Oxford).
  • Brennan, M.J. and Schwartz, E.S., The valuation of American put options. J. Financ., 1977, 32, 449–462. doi:10.1111/j.1540-6261.1977.tb03284.x.
  • Caldana, R., Fusai, G., Gnoatto, A. and Graselli, M., General close-form basket option pricing bounds. Quant. Finance, 2016, 16, 535–554. doi:10.1080/14697688.2015.1073854.
  • Carslow, H.S. and Jaeger, J.C., Conduction of Heat in Solids, 1959 (Clarendon Press: Oxford).
  • Chen, X., Deelstra, G., Dhaene, J., Linders, D. and Vanmaele, M., On an optimization problem related to static super-replicating strategies. J. Comput. Appl. Math., 2015, 278, 213–230. doi:10.1016/j.cam.2014.10.003.
  • Chen, X., Deelstra, G., Dhaene, J. and Vanmaele, M., Static super-replicating strategies for a class of exotic options. Insur. Math. Econ., 2008, 42, 1067–1085. doi:10.1016/j.insmatheco.2008.01.002.
  • Clift, S.S. and Forsyth, P.A., Numerical solution of two asset jump diffusion models for option valuation. Appl. Numer. Math., 2008, 58, 743–782. doi:10.1016/j.apnum.2007.02.005.
  • Company, R., Egorova, V., Jódar, L. and Soleymani, F., A mixed derivative terms removing method in multi-asset option pricing problems. Appl. Math. Lett., 2016, 60, 108–114. doi:10.1016/j.aml.2016.04.011.
  • Crank, J., The Mathematics of Diffusion, 1979 (Oxford University Press: Oxford).
  • Crank, J. and Nicolson, P., A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proceedings of the Cambridge Philosophical Society, Vol. 43, pp. 50–67, 1947.
  • Deelstra, G., Diallo, I. and Vanmaele, M., Bounds for Asian basket options. J. Comput. Appl. Math., 2008, 218, 215–228. doi:10.1016/j.cam.2006.12.017.
  • Deelstra, G., Liinev, J. and Vanmaele, M., Pricing of arithmetic basket options by conditioning. Insur. Math. Econ., 2004, 34, 55–77. doi:10.1016/j.insmatheco.2003.11.002.
  • Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. and Vyncke, D., The concept of comonotonicity in actuarial science and finance: Theory. Insur. Math. Econ., 2002a, 31, 3–33. doi:10.1016/S0167-6687(02)00134-8.
  • Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. and Vyncke, D., The concept of comonotonicity in actuarial science and finance: Applications. Insur. Math. Econ., 2002b, 31, 133–161. doi:10.1016/S0167-6687(02)00135-X.
  • Dhaene, J., Kukush, A. and Linders, D., The multivariate Black & Scholes market: Conditions for completeness and no-arbitrage. Theory Probab. Math. Stat., 2014, 88, 85–98. doi:10.1090/S0094-9000-2014-00920-5.
  • Dhaene, J., Kukush, A. and Linders, D., Comonotonic asset prices in arbitrage-free markets. Working Paper, Leuven, KU Leuven—Faculty of Business and Economics, 2018.
  • Dhaene, J., Wang, S., Young, V. and Goovaerts, M.J., Comonotonicity and maximal stop-loss premiums. Bulletin of the Swiss Association of Actuaries, 2000, 5, 99–113.
  • Duffy, D., A critique of the Crank-Nicolson scheme. Wilmott Magazine, July 2004, 68–77.
  • Düring, B. and Heuer, C., High-order compact schemes for parabolic problems with mixed derivatives in multiple space dimensions. SIAM. J. Numer. Anal., 2015, 53, 2113–2134. doi:10.1137/140974833.
  • Escobar, M., Krause, D. and Zagst, R., Stochastic covariance and dimension reduction in the pricing of basket options. Rev. Deriv. Res., 2016, 19(3), 165–200. doi: 10.1007/s11147-016-9119-x
  • Haentjens, T. and In't Hout, K.J., ADI schemes for pricing American options under the Heston model. Appl. Math. Financ., 2015, 22, 207–237. doi:10.1080/1350486X.2015.1009129.
  • Hainaut, D. and Deelstra, G., Default probabilities of a holding company, with complete and partial information. J. Comput. and Appl. Math., 2014, 271, 380–400. doi: 10.1016/j.cam.2014.04.003
  • Hill, J.M. and Dewynne, J.N., Heat Conduction, 1987 (Blackwell Scientific: Oxford [Oxfordshire]; Boston).
  • Kaas, R., Dhaene, J. and Goovaerts, M.J., Upper and lower bounds for sums of random variables. Insur. Math. Econ., 2000, 27, 151–168. doi:10.1016/S0167-6687(00)00060-3.
  • Krekel, M., de Kock, J., Korn, R. and Man, T.-K., An analysis of pricing methods for baskets options. The Best of Wilmott, 2006, 2, 181–188.
  • Leentvaar, C.C.W. and Oosterlee, C.W., Multi-asset option pricing using a parallel Fourier-based technique. J. Comput. Financ., 2008, 12, 1–26. doi:10.21314/JCF.2008.184.
  • Linders, D., Pricing index options in a multivariate Black & Scholes model, Research Report AFI-1383, FEB, KU, Leuven, 2013.
  • Linders, D. and Stassen, B., The multivariate Variance Gamma model: Basket option pricing and calibration. Quant. Finance, 2016, 16, 555–572. doi:10.1080/14697688.2015.1043934.
  • Longstaff, F.A. and Schwarts, E.S., Valuing American options by simulations: A simple Least-Squares approach. Rev. Financ. Stud., 2001, 14, 113–147. doi: 10.1093/rfs/14.1.113
  • Musiela, M. and Rutkowski, M., Martingale Methods in Financial Modelling (2nd ed.), 2005 (Springer-Verlag: Berlin).
  • R Core Team, R: A Language and Environment for Statistical Computing, 2017 (R Foundation for Statistical Computing: Vienna, Austria). https://www.R-project.org/.
  • Reisinger, C. and Wittum, G., Efficient hierarchical approximation of high-dimensional option pricing problems. SIAM J. Sci. Comput., 2007, 29, 440–458. doi:10.1137/060649616.
  • Simon, S., Goovaerts, M.J. and Dhaene, J., An easy computable upper bound for the price of an arithmetic Asian option. Insur. Math. Econ., 2000, 26, 175–183. doi:10.1016/S0167-6687(99)00051-7.
  • Venables, W.N. and Ripley, B.D., Modern Applied Statistics with S (4th ed.), 2002 (Springer: New York). ISBN 0-387-95457-0. http://www.stats.ox.ac.uk/pub/MASS4.
  • Vyncke, D., Goovaerts, M. and Dhaene, J., An accurate analytical approximation for the price of a European-style arithmetic Asian option. Finance, 2004, 25, 121–139.
  • Wang, Y. and Caflisch, R., Pricing and hedging american-style options: A simple simulation-based approach. J. Comput. Financ., 2010, 13(4), 95–125. doi: 10.21314/JCF.2010.220
  • Wilmott, P., Paul Wilmott on Quantitative Finance (2nd ed), 2006 (John Wiley & Sons: Chichester).
  • Wilmott, P., Dewynne, J. and Howison, S., Option Pricing: Mathematical Models and Computation, 1994 (Oxford Financial Press: Oxford).
  • Witelski, T.P. and Bowen, M., ADI schemes for higher-order nonlinear diffusion equations. Appl. Numer. Math., 2003, 45, 331–351. doi:10.1016/S0168-9274(02)00194-0.
  • Zvan, R., Forsyth, P.A. and Vetzal, K., Robust numerical methods for PDE models of Asian options. J. Comput. Financ., 1998, 1, 39–78. doi:10.21314/JCF.1997.006.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.