DEJDDouble Exponential Jump-Diffusion (economic model)
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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).
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.
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].
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.
If we set the Lee-Carter model as the benchmark and compare the Chen-Cox model and the DEJD models, we conclude the following.
Compared to the Lee-Carter model, our DEJD model considers the possibility of both positive jumps and negative jumps in the jump diffusion process, not in the baseline Brownian motion process.
The jump diffusion component in our model applies the compound Poisson DEJD to extend the Lee-Carter model so as to describe longevity jumps (negative jumps) and mortality jumps (positive jumps) separately.
We calibrated our model with the historical mortality rate data 1900-2004 from National Center for Health Statistics and we compared the prices of the q-forward fixed rate, calculated by the Lee-Carter model, the Chen-Cox model, and our DEJD model.