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Absolute Diffusion Process: Sensitivity Measures

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Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

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Abstract

The constant elasticity of variance (CEV) model of Cox (Notes on Option Pricing I: Constant Elasticity of Variance Diffusions. Working paper, Stanford University (1975)) captures the implied volatility smile that is similar to the volatility curves observed in practice. This diffusion process has been used for pricing several financial option contracts. In this paper we present the analytical expressions of sensitivity measures for the absolute diffusion process, commonly known as Greeks, and we analyze numerically the behavior of the measures for European options under the CEV model.

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Notes

  1. 1.

    Equation (11) of Proposition 1 is standard in the literature and can be found, for example, in [5]. Equation (12) is then easily obtained through the put–call parity relation.

  2. 2.

    Due to constraints of space, we have not included proofs of the analytical expressions of sensitivity measures, but they are available upon request.

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Acknowledgements

Dias is member of the BRU-UNIDE, and Braumann and Larguinho are members of the Research Center Centro de Investigação em Matemática e Aplicações (CIMA), both centers financed by the Fundação para a Ciência e Tecnologia (FCT). Dias gratefully acknowledges the financial support from the FCTs grant number PTDC/EGE-ECO/099255/2008.

Author information

Authors and Affiliations

  1. Centro de Investigação em Matemática e Aplicações, Universidade de Évora and Department of Mathematics, ISCAC, Quinta Agrícola, Bencata, 3040-316, Coimbra, Portugal

    Manuela Larguinho

  2. BRU-UNIDE and ISCTE-IUL Business School, Complexo INDEG/ISCTE, Av. Prof. Aníbal Bettencourt, 1600-189, Lisboa, Portugal

    José Carlos Dias

  3. Centro de Investigação em Matemática e Aplicações, Universidade de Évora, Rua Romão Ramalho 59, 7000-671, Évora, Portugal

    Carlos A. Braumann

Authors
  1. Manuela Larguinho
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  2. José Carlos Dias
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  3. Carlos A. Braumann
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Corresponding author

Correspondence to Manuela Larguinho .

Editor information

Editors and Affiliations

  1. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    João Lita da Silva

  2. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    Frederico Caeiro

  3. , Universidade Nova de Lisboa, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica, Caparica, 2829-516, Portugal

    Isabel Natário

  4. , Universidade Nova de Lisboa,, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica 59, Caparica, 2829-516, Portugal

    Carlos A. Braumann

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Larguinho, M., Dias, J.C., Braumann, C.A. (2013). Absolute Diffusion Process: Sensitivity Measures. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34904-1_26

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