Valuing equity-linked death benefits in a regime-switching framework

In this article, we consider the problem of computing the expected discounted
value of a death benefit, e.g. in Gerber et al. (2012, 2013), in a regime-switching
economy. Contrary to their proposed discounted density approach, we adopt
the Laplace transform to value the contingent options. By this alternative approach, closed-form expressions for the Laplace transforms of the values of
various contingent options, such as call/put options, lookback options, barrier
options, dynamic fund protection and the dynamic withdrawal benefits, have
been obtained. The value of each contingent option can then be recovered by
the numerical Laplace inversion algorithm, and this efficient approach is documented by several numerical illustrations. The strength of our methodology
becomes apparent when we tackle the valuations of exotic contingent options
in the cases when (1) the contracts have a finite expiry date; (2) when the timeuntil-death variable is uniformly distributed in accordance with De Moivre’s
law.