DEJDDouble Exponential Jump-Diffusion (economic model)
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Next, the DEJD model is compared with both Lee-Carter Brownian motion model and the normal jump diffusion model (Chen and Cox, 2009).
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).
The underlying reasons that our DEJD model fits the data better are as follows.
The Lee-Carter model, the Chen-Cox model and our DEJD model will naturally yield different values for the best estimate mortality projection.
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.
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].
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.
Kou and Wang (2004) discuss derivative pricing using the DEJD model for security prices, and they derive the risk-neutral measure for this stochastic process.
t] distribution, the analysis here incorporates a DEJD model to capture both the positive jumps and negative jumps of the [k.
Because of this closed-form solution, the DEJD model may provide a useful stochastic mortality model for internal company mortality simulation as well as being useful in the capital market applications we discuss subsequently.
Figure 5 shows how the DEJD model fits the actual increment of mortality rate [DELTA][k.