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Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods

  • Jan Baldeaux
  • Eckhard Platen

We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the finance problem under consideration require e.g. continuous monitoring of the processes, the simulation algorithm can easily be embedded in a multilevel Monte Carlo scheme. We choose to introduce the finance problems under the benchmark approach, and find that this approach allows us to exploit conveniently the analytical tractability of these diffusion processes.

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File URL: http://arxiv.org/pdf/1204.1126
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Paper provided by arXiv.org in its series Papers with number 1204.1126.

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Date of creation: Apr 2012
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Handle: RePEc:arx:papers:1204.1126
Contact details of provider: Web page: http://arxiv.org/

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  1. David Heath & Eckhard Platen, 2005. "Currency Derivatives Under A Minimal Market Model With Random Scaling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1157-1177.
  2. Jan Baldeaux & Dale Roberts, 2012. "Quasi-Monte Carlo methods for the Heston model," Papers 1202.3217, arXiv.org, revised May 2012.
  3. Jan Baldeaux & Katja Ignatieva & Eckhard Platen, 2012. "A Tractable Model for Indices Approximating the Growth Optimal Portfolio," Research Paper Series 318, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Da Fonseca José & Grasselli Martino & Ielpo Florian, 2014. "Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 37, May.
  5. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
  6. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, vol. 10(2), pages 151-180, May.
  7. Mark Craddock & Eckhard Platen, 2003. "Symmetry Group Methods for Fundamental Solutions and Characteristic Functions," Research Paper Series 90, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, 02.
  9. José Da Fonseca & Martino Grasselli & Florian Ielpo, 2011. "Hedging (Co)Variance Risk With Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 899-943.
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