DEJDDouble Exponential Jump-Diffusion (economic model)
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Preliminary computations using this methodology using the DEJD mortality table model show that the resulting life settlement price is indeed changed to reflect risk.
The DEJD model for [dk.sub.t] faces the same problem.
Figure 5 shows how the DEJD model fits the actual increment of mortality rate [DELTA][k.sub.t], by comparing the distribution generated by the DEJD model calibrated to historical data and the actual distribution of [DELTA][k.sub.t].
Next, the DEJD model is compared with both Lee-Carter Brownian motion model and the normal jump diffusion model (Chen and Cox, 2009).
The underlying reasons that our DEJD model fits the data better are as follows.
However, if the 1918 flu year is excluded and the series is made artificially smoother, then using the BIC criterion, the parameter penalty dominates and the ranking is simply according to the number of parameters in the model (Lee-Carter with two parameters, then Chen-Cox with five parameters, and then DEJD model with six parameters).
However, the mortality rate in our model for a fixed age is itself linearly dependent on the time series [k.sub.t], that we modeled using the DEJD. In an incomplete market, the risk neutral pricing will allow pricing of the derivative.
In this article, we use the Swiss Re mortality catastrophe bond to determine a known market price of mortality risk to enable us to calculate [zeta], and then use this in our DEJD model to price the q-forward incorporating [zeta] as an implementation example of our DEJD model.
Based on the known 2003 mortality time series, simulate 10,000 times the future mortality time-series k(t) for 2004-2006, using the DEJD model (5) with the calibrated parameter set {lambda, p; [[eta].sub.1], [[eta].sub.2]; [alpha], [sigma]} = {0.064, 0.45; 0.71, 0.75; -0.20; 0.31}, and the initial assumed set [zeta] = {[[eta].sub.1], [[eta].sub.2], [[eta].sub.3]} = {0, 0, 0}, with the risk-neutral transform function.
Based on our DEJD model and the q-forward product structure above, the fixed rate can be calculated with the closed-form formula (19) directly:
This DEJD pricing may differ from that of the Lee--Carter or Chen-Cox models.
The Lee-Carter model, the Chen-Cox model and our DEJD model will naturally yield different values for the best estimate mortality projection.