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Malliavin calculus in finance

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Author Info

  • Arturo Kohatsu
  • Montero Miquel

Abstract

This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.

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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 672.

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Date of creation: Apr 2003
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Handle: RePEc:upf:upfgen:672

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Web page: http://www.econ.upf.edu/

Related research

Keywords: Malliavin claculus; computational finance; Greeks; Monte Carlo methods; kernel density method;

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References

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  1. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151.
  3. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
  4. Guillaume Bernis & Emmanuel Gobet & Arturo Kohatsu-Higa, 2003. "Monte Carlo Evaluation of Greeks for Multidimensional Barrier and Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 99-113.
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Citations

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Cited by:
  1. Nicola Cufaro Petroni & Piergiacomo Sabino, 2013. "Multidimensional quasi-Monte Carlo Malliavin Greeks," Decisions in Economics and Finance, Springer, vol. 36(2), pages 199-224, November.
  2. Nicola Cufaro Petroni & Piergiacomo Sabino, 2011. "Multidimensional Quasi-Monte Carlo Malliavin Greeks," Papers 1103.5722, arXiv.org.
  3. Leão, Dorival & Ohashi, Alberto, 2012. "Weak Approximations for Wiener Functionals," Insper Working Papers wpe_276, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  4. Leão, Dorival & Ohashi, Alberto, 2010. "Weak Approximations for Wiener Functionals," Insper Working Papers wpe_215, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  5. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
  6. Chen, Nan & Glasserman, Paul, 2007. "Malliavin Greeks without Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1689-1723, November.

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