Do Jumps Matter in the Long Term? A Tale of Two Horizons

<?xml version="1.0" encoding="UTF-8"?><collection xmlns="" xmlns:xsi="" xsi:schemaLocation="">
    <leader>00000cab a2200000   4500</leader>
    <controlfield tag="001">MAP20220008549</controlfield>
    <controlfield tag="003">MAP</controlfield>
    <controlfield tag="005">20220315125545.0</controlfield>
    <controlfield tag="008">220315e20220307esp|||p      |0|||b|spa d</controlfield>
    <datafield tag="040" ind1=" " ind2=" ">
      <subfield code="a">MAP</subfield>
      <subfield code="b">spa</subfield>
      <subfield code="d">MAP</subfield>
    <datafield tag="084" ind1=" " ind2=" ">
      <subfield code="a">6</subfield>
    <datafield tag="100" ind1=" " ind2=" ">
      <subfield code="0">MAPA20190008310</subfield>
      <subfield code="a">Bégin, Jean-François</subfield>
    <datafield tag="245" ind1="1" ind2="0">
      <subfield code="a">Do Jumps Matter in the Long Term? A Tale of Two Horizons</subfield>
      <subfield code="c">Jean-François Bégin, Mathieu Boudreault</subfield>
    <datafield tag="520" ind1=" " ind2=" ">
      <subfield code="a">Economic scenario generators (ESGs) for equities are important components of the valuation and risk management process of life insurance and pension plans. Because the resulting liabilities are very long-lived and the short-term performance of the assets backing these liabilities may trigger important losses, it is thus a desired feature of an ESG to replicate equity returns over such horizons. In light of this horizon duality, we investigate the relevance of jumps in ESGs to replicate dynamics over different horizons and compare their performance to popular models in actuarial science. We show that jump-diffusion models cannot replicate higher moments if estimated with the maximum likelihood. Using a generalized method of momentsbased approach, however, we find that simple jump-diffusion models have an excellent fit overall (moments and the entire distribution) at different timescales. We also investigate three typical applications: the value of $1 accumulated with no intermediate monitoring, a solvency analysis with frequent monitoring, and a dynamic portfolio problem. We find that jumps have long-lasting effects that are difficult to replicate otherwise, so, yes, jumps do matter in the long term.

    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080591182</subfield>
      <subfield code="a">Gerencia de riesgos</subfield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080579258</subfield>
      <subfield code="a">Cálculo actuarial</subfield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080611897</subfield>
      <subfield code="a">Perspectivas económicas</subfield>
    <datafield tag="700" ind1=" " ind2=" ">
      <subfield code="0">MAPA20090011267</subfield>
      <subfield code="a">Boudreault, Mathieu</subfield>
    <datafield tag="773" ind1="0" ind2=" ">
      <subfield code="w">MAP20077000239</subfield>
      <subfield code="g">07/03/2022 Tomo 26 Número 1 - 2022 , p. 82- 101</subfield>
      <subfield code="x">1092-0277</subfield>
      <subfield code="t">North American actuarial journal</subfield>
      <subfield code="d">Schaumburg : Society of Actuaries, 1997-</subfield>