243
Views
7
CrossRef citations to date
0
Altmetric
Articles

American option pricing under double Heston stochastic volatility model: simulation and strong convergence analysis

&
Pages 1322-1339 | Received 04 Aug 2018, Accepted 30 Jan 2019, Published online: 13 Feb 2019

References

  • Rego AT, dos Santos TR. Non-Gaussian stochastic volatility model with jumps via Gibbs sampler. Available from https://arxiv.org/pdf/1809.01501.pdf
  • Heston SL. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev Financ Stud. 1993;6:327–343. doi: 10.1093/rfs/6.2.327
  • Bates DS. Jumps and stochastic volatility: the exchange rate processes implicit in deutsche mark options. Rev Financ Stud. 1996;9:69–107. doi: 10.1093/rfs/9.1.69
  • Benhamou E, Gobet E, Miri M. Time dependent Heston model. SIAM J Financ Math. 2010;1:289–325. doi: 10.1137/090753814
  • Chesney M, Scott L. Pricing European currency options: a comparison of the modified Black-Scholes model and a random variance model. J Finan Quant Anal. 1989;24(3):267–284. doi: 10.2307/2330812
  • Hull J, White A. The pricing of options on assets with stochastic volatilities. J Finance. 1987;42(2):281–300. doi: 10.1111/j.1540-6261.1987.tb02568.x
  • Schobel R, Zhu JW. Stochastic volatility with an Ornstein-Uhlenbeck process: an extension. Eur Finance Rev. 1999;3(1):23–46. doi: 10.1023/A:1009803506170
  • Christoffersen P, Heston S, Jacobs K. The shape and term structure of the index option smirk: why multi factor stochastic volatility models work so well. Manage Sci. 2009;55(12):1914–1932. doi: 10.1287/mnsc.1090.1065
  • Cont R, Tankov P. Financial modelling with jump processes. Boca Raton (FL): Chapman and Hall/CRC Press; 2004.
  • da Fonseca J, Grasselli M, Tebaldi C. A multi factor volatility Heston model. Quant Finance. 2008;8(6):591–604. doi: 10.1080/14697680701668418
  • Fouque JP, Lorig MJ. A fast mean-reverting correction to Heston's stochastic volatility model. SIAM J Financ Math. 2011;2(1):221–254. doi: 10.1137/090761458
  • Mehrdoust F, Saber N. Pricing arithmetic Asian option under a two-factor stochastic volatility model with jumps. J Stat Comput Simul. 2015;85(18):3811–3819. doi: 10.1080/00949655.2015.1046072
  • Gourieroux C. Continuous time Wishart process for stochastic risk. Econom Rev. 2007;25:177–217. doi: 10.1080/07474930600713234
  • Najafi AR, Mehrdoust F. Bond pricing under mixed generalized CIR model with mixed Wishart volatility process. J Comput Appl Math. 2017;319(C):108–116. doi: 10.1016/j.cam.2016.12.039
  • Li G, Zhang C. On the number of state variables in option pricing. Manage Sci. 2010;56(11):2058–2075. doi: 10.1287/mnsc.1100.1222
  • Albrecher H, Mayer P, Schoutens W, et al. The little Heston trap. Wilmott Magazine; 2007. p. 83–92.
  • AitSahlia F, Goswami M, Guha S. American option pricing under stochastic volatility: an empirical evaluation. Comput Manag Sci. 2008;7:789–206.
  • Broadie M, Glasserman P. Pricing American-style securities using simulation. J Econ Dyn Control. 1997;21:1323–1352. doi: 10.1016/S0165-1889(97)00029-8
  • Longstaff FA, Schwartz ES. Valuing American put options by simulation: a simple least squares approach. Rev Financ Stud. 2001;14(1):113–147. doi: 10.1093/rfs/14.1.113
  • Stentoft L. Assessing the least squares Monte-Carlo approach to American option valuation. Rev Deriv Res. 2004;(7):129–168. doi: 10.1023/B:REDR.0000031176.24759.e6
  • Morales M. Implementing importance sampling in the least-squares Monte Carlo approach for American options, HERMIS-μπ. Hellenic European Research on Mathematics and Informatics Science; 2006. Available at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.549.321&rep=rep1&type=pdf.
  • Glasserman P. Monte Carlo methods in financial engineering. New York (NY): Springer-Verlag; 2003.
  • Higham DJ, Mao X, Stuart AM. Strong convergence of Euler type methods for nonlinear stochastic differential equations. SIAM J Numer Anal. 2002;40(3):1041–1063. doi: 10.1137/S0036142901389530
  • Karatzas I, Shreve SE. Brownian motion and stochastic calculus. New York (NY): Springer; 1988.
  • Mao X. stochastic differential equation and applications. Chichester: Horwood; 1997.
  • Oksendal B. Stochastic differential equations: an introduction with applications. 5th ed. New York (NY): Springer; 1995.
  • Oguntuase JA. On an inequality of Gronwall. J Ineq Pure Appl Math. 2001;2(1).

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.