Advanced search
Publication Cover
Quantitative Finance Volume 16, 2016 - Issue 2: Stochastic Optimization Approaches to Financial and Energy Markets
Submit an article Journal homepage
236
Views
2
CrossRef citations to date
0
Altmetric
Research Papers

Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation

Georg Ch. PflugDepartment of Statistics and Operations Research, University of Vienna, Oskar Morgenstern Platz 1, 1090Vienna, Austria.;IIASA, Laxenburg, Austria.Correspondence[email protected]
View further author information
&
Philipp ThomaDepartment of Statistics and Operations Research, University of Vienna, Oskar Morgenstern Platz 1, 1090Vienna, Austria.View further author information
Pages 247-257 | Received 14 Nov 2013, Accepted 05 Jul 2015, Published online: 01 Feb 2016

References

  • Capriotti, L., Fast Greeks by algorithmic differentiation. J. Comput. Finance, 2011, 14(3), 3–35.
  • Fu, M., Variance-Gamma and Monte Carlo. In Advances in Mathematical Finance, edited by M. Fu, R.A. Jarrow, J.-Y. Yen and R.J. Elliott, pp. 21–35, 2007 (Birkhauser: Boston).
  • Glasserman, P., Monte Carlo Methods in Financial Engineering, Stochastic Modelling in Applied Probability, 2004 (Springer Verlag: New York).
  • Glasserman, P. and Liu, Z., Estimating Greeks in simulating Lévy-driven models. J. Comput. Finance, 2010, 14(2), 3–55.
  • Glynn, P. and Whitt, W., The asymptotic efficiency of simulation estimators. Oper. Res., 1992, 40(3), 505–520.
  • Heidergott, B. and Hordijk, A., Single-run gradient estimation via measure-valued differentiation. IEEE Trans. Autom. Control, 2004, 49(10), 1843–1847.
  • Heidergott, B. and Leahu, H., Weak differentiability of product measures. Math. Oper. Res., 2010, 35, 27–51.
  • Heidergott, B. and Vazquez-Abad, F.J., Measure-valued differentiation for random horizon problems. Markov Process. Relat. Fields, 2006, 12, 509–536.
  • Heidergott, B., Vazquez-Abad, F.J., Pflug, G.Ch. and Farenhorst-Yuan, T., Gradient estimation for discrete-event systems by measure-valued differentiation. ACM Trans. Model. Comput. Simul. (TOMACS), 2010, 20(1), 5:1–5:28.
  • Heidergott, B., Vazquez-Abad, F.J. and Volk-Makarewicz, W., Sensitivity estimation for Gaussian systems. Eur. J. Oper. Res., 2008, 187, 193–207.
  • Hull, J.C., Fundamentals of Futures and Options Markets, 5th ed., 2005 (Pearson Education: Frenchs Forest).
  • Miyahara, Y., Martingale measures for the geometric Lévy models. Discussion Papers in Economics, No. 431, Nagoya City University, 2005.
  • Montero, M. and Kohatsu-Higa, A., Malliavin calculus applied to finance. Physica, 2003, 320, 548–570.
  • Pflug, G.Ch., Optimization of Stochastic Models, 1996 (Kluwer Academic: Dordrecht).
  • Sanz-Sole, M., Malliavin Calculus, 2005 (EPFL Press: Lausanne).
  • Schoutens, W., Lévy Processes in Finance. Wiley Series in Probability and Statistics, 2003 (J. Wiley and Sons: Chichester).
  • Vazquez-Abad, F.J. and Heidergott, B., Measure-valued differentiation for Markov Chains. J. Optim. Theory Appl., 2008, 136, 187–209.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.