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A Contingent Claim Analysis of Suicide

  • Shin S. Ikeda

    (National Graduate Institute for Policy Studies)

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    An option-theoretic model of suicide in the continuous time framework is proposed. Given completeness of the financial market and the associated contingent claim argument, the value of human capital consistent with the no-arbitrage principle is determined as the expected, discounted, present value of the future wage stream under the risk-neutral probability measure. The suicide option - the right but not the obligation to commit suicide - is modelled as an American put option with this human capital stock and a certain reference level of human capital as the underlier and strike price, respectively. The value of underlier falling short of the srtike price doet not induce the option holder's immediate suicide because of the option value to postpone such a fatal and irreversible decision. This value, the delayed exercise premium, is given in a near closed form up to a deterministic exercise boundary. The nearly closed-form nature of this boundry allows one to calibrate the model to the real suicide rates among Japanese male workers from 1998 to 2009. The calibrated value of the strike price roughly amounts to the perpetual annuity value of the 90 percentage of the initial wage earned as of the new entry into the labor market, with the coupon rate given by the spread in market prices of risk between financial and labor market.

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    Paper provided by National Graduate Institute for Policy Studies in its series GRIPS Discussion Papers with number 13-05.

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    Length: 26 pages
    Date of creation: May 2013
    Date of revision:
    Handle: RePEc:ngi:dpaper:13-05
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    1. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2007. "Portfolio Choice over the Life-Cycle when the Stock and Labor Markets Are Cointegrated," Journal of Finance, American Finance Association, vol. 62(5), pages 2123-2167, October.
    2. Chan, Leo & Lien, Donald, 2010. "The value of planned death," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 39(6), pages 692-695, December.
    3. Bodie, Zvi & Detemple, Jerome B. & Otruba, Susanne & Walter, Stephan, 2004. "Optimal consumption-portfolio choices and retirement planning," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1115-1148, March.
    4. Zvi Bodie & J�r�me Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    5. Mary C. Daly & Daniel J. Wilson & Norman J. Johnson, 2007. "Relative status and well-being: evidence from U.S. suicide deaths," Working Paper Series 2007-12, Federal Reserve Bank of San Francisco.
    6. Hamermesh, Daniel S & Soss, Neal M, 1974. "An Economic Theory of Suicide," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 83-98, Jan.-Feb..
    7. Merton, Robert C., 1997. "Applications of Option-Pricing Theory: Twenty-Five Years Later," Nobel Prize in Economics documents 1997-1, Nobel Prize Committee.
    8. McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
    9. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2007. "Portfolio choice over the life-cycle when the stock and labor markets are cointegrated," Working Paper Series WP-07-11, Federal Reserve Bank of Chicago.
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