Details
| Original language | English |
|---|---|
| Pages (from-to) | 1481 - 1517 |
| Number of pages | 37 |
| Journal | Bernoulli |
| Volume | 23 |
| Issue number | 3 |
| Publication status | Published - Aug 2017 |
| Externally published | Yes |
Abstract
The paper derives saddlepoint expansions for conditional expectations in the form of E[X|Y ≥ a] and E[X|Y ≥ a] for the sample mean of a continuous random vector (X, Y) 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.
Keywords
- Conditional expectation, Risk management, Saddlepoint approximation, Sensitivity estimation
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
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In: Bernoulli, Vol. 23, No. 3, 08.2017, p. 1481 - 1517.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - Saddlepoint methods for conditional expectations with applications to risk management
AU - Kim, Sojung
AU - Kim, Kyoung-Kuk
N1 - Publisher Copyright: © 2017 ISI/BS.
PY - 2017/8
Y1 - 2017/8
N2 - The paper derives saddlepoint expansions for conditional expectations in the form of E[X|Y ≥ a] and E[X|Y ≥ a] for the sample mean of a continuous random vector (X, Y) 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.
AB - The paper derives saddlepoint expansions for conditional expectations in the form of E[X|Y ≥ a] and E[X|Y ≥ a] for the sample mean of a continuous random vector (X, Y) 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.
KW - Conditional expectation
KW - Risk management
KW - Saddlepoint approximation
KW - Sensitivity estimation
UR - http://www.scopus.com/inward/record.url?scp=85016189457&partnerID=8YFLogxK
U2 - 10.3150/15-BEJ774
DO - 10.3150/15-BEJ774
M3 - Article
VL - 23
SP - 1481
EP - 1517
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 3
ER -