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August 2017 Saddlepoint methods for conditional expectations with applications to risk management
Sojung Kim, Kyoung-Kuk Kim
Bernoulli 23(3): 1481-1517 (August 2017). DOI: 10.3150/15-BEJ774


The paper derives saddlepoint expansions for conditional expectations in the form of $\mathsf{E}[\overline{X}|\overline{\mathbf{Y}}=\mathbf{a}]$ and $\mathsf{E}[\overline{X}|\overline{\mathbf{Y}}\geq\mathbf{a}]$ for the sample mean of a continuous random vector $(X,\mathbf{Y}^{\top})$ whose joint moment generating function is available. Theses conditional expectations frequently appear in various applications, particularly in quantitative finance and risk management. Using the newly developed saddlepoint expansions, we propose fast and accurate methods to compute the sensitivities of risk measures such as value-at-risk and conditional value-at-risk, and the sensitivities of financial options with respect to a market parameter. Numerical studies are provided for the accuracy verification of the new approximations.


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Sojung Kim. Kyoung-Kuk Kim. "Saddlepoint methods for conditional expectations with applications to risk management." Bernoulli 23 (3) 1481 - 1517, August 2017.


Received: 1 July 2015; Revised: 1 September 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714309
MathSciNet: MR3624868
Digital Object Identifier: 10.3150/15-BEJ774

Keywords: conditional expectation , risk management , saddlepoint approximation , sensitivity estimation

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability


Vol.23 • No. 3 • August 2017
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