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An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks.

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Τίτλος: An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks.
Συγγραφείς: Zhao, Yixing1, Mamon, Rogemar1,2 rmamon@stats.uwo.ca
Πηγή: Insurance: Mathematics & Economics. Jan2018, Vol. 78, p1-12. 12p.
Θεματικοί όροι: *Mortality -- Mathematical models, *Derivative securities, *Mathematical models of interest rates, *Monte Carlo method, Mathematics in insurance
Περίληψη: We introduce a pricing framework for a guaranteed annuity option (GAO) where both the interest and mortality risks are correlated. We assume that the short rate and the force of mortality follow the Cox–Ingersoll–Ross (CIR) and Lee–Carter models, respectively. Employing the change of measure technique, we decompose the pure endowment into the product of the bond price and survival probability, thereby facilitating the evaluation of the annuity expression. With the aid of the dynamics of interest and mortality processes under the forward measure, we construct an algorithm based on comonotonicity theory to estimate the quantiles of survival probability and annuity rate. The comonotonic upper and lower bounds in the convex order are used to approximate the annuity and GAO prices and henceforth avoiding the simulation-within-simulation problem. Numerical illustrations show that our algorithm gives an efficient and practical method to estimate GAO values. [ABSTRACT FROM AUTHOR]
Copyright of Insurance: Mathematics & Economics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks.
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  Data: <searchLink fieldCode="JN" term="%22Insurance%3A+Mathematics+%26+Economics%22">Insurance: Mathematics & Economics</searchLink>. Jan2018, Vol. 78, p1-12. 12p.
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  Data: *<searchLink fieldCode="DE" term="%22Mortality+--+Mathematical+models%22">Mortality -- Mathematical models</searchLink><br />*<searchLink fieldCode="DE" term="%22Derivative+securities%22">Derivative securities</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+models+of+interest+rates%22">Mathematical models of interest rates</searchLink><br />*<searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+in+insurance%22">Mathematics in insurance</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: We introduce a pricing framework for a guaranteed annuity option (GAO) where both the interest and mortality risks are correlated. We assume that the short rate and the force of mortality follow the Cox–Ingersoll–Ross (CIR) and Lee–Carter models, respectively. Employing the change of measure technique, we decompose the pure endowment into the product of the bond price and survival probability, thereby facilitating the evaluation of the annuity expression. With the aid of the dynamics of interest and mortality processes under the forward measure, we construct an algorithm based on comonotonicity theory to estimate the quantiles of survival probability and annuity rate. The comonotonic upper and lower bounds in the convex order are used to approximate the annuity and GAO prices and henceforth avoiding the simulation-within-simulation problem. Numerical illustrations show that our algorithm gives an efficient and practical method to estimate GAO values. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Insurance: Mathematics & Economics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.insmatheco.2017.09.001
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 1
    Subjects:
      – SubjectFull: Mortality -- Mathematical models
        Type: general
      – SubjectFull: Derivative securities
        Type: general
      – SubjectFull: Mathematical models of interest rates
        Type: general
      – SubjectFull: Monte Carlo method
        Type: general
      – SubjectFull: Mathematics in insurance
        Type: general
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      – TitleFull: An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks.
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            NameFull: Zhao, Yixing
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            NameFull: Mamon, Rogemar
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            – D: 01
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              Text: Jan2018
              Type: published
              Y: 2018
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              Value: 78
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            – TitleFull: Insurance: Mathematics & Economics
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