A Contingent Claim Analysis of Suicide
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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