Mortality Modeling & Forecasting
Description

Longevity risk arises from the following two sources of uncertainty:

"Diffusion Risk": the variation surrounding the trend in future mortality;

"Drift Risk": the uncertainty about the trend itself.


Traditional mortality models capture only "diffusion risk", but not "drift risk".

The locally linear CairnsBlakeDowd (LLCBD) model is designed to quantify "drift risk" in addition to "diffusion risk".

In LLCBD model, we permit the drifts of the expected mortality trend to be random.

The Kalman filtering technique is used to estimate the parameters.

The resulting forecasts are more consistent with the recent trends.

Description
Illustration
The 95% prediction intervals of the period effects in the original CBD model (in yellow) and the LLCBD model (in blue).
Illustration
Related Paper

Liu, Y. and Li, J.S.H., 2017. The locallylinear CairnsBlakeDowd model: A note on deltanuga hedging of longevity risk. ASTIN Bulletin 47: 79151.
Related Paper
LLCBD MODEL
Description

The heat wave model is designed to capture both longterm and shortterm mortality improvements, and to produce twodimensional improvement scales with minimal subjective judgement.

Shortterm mortality improvements are treated as `heat waves' that taper off over time.

Longterm mortality improvements are treated as `background improvements' that always exist.

Estimation can be achieved through MLE, and the uncertainty of the forecast of mortality improvement rates can be quantified.

Description
Illustration
The heat map of the expected mortality improvement rates implied by the heat wave model.
Illustration
HEAT WAVE MODEL
Related Paper

Li, J.S.H., and Liu, Y., 2018. The Heat Wave Model for Constructing TwoDimensional Mortality Improvement Scales with Measures of Uncertainty. Under Review.
Related Paper
Description

The dynamics of human mortality over time are subject to shortterm jumps (e.g., influenza pandemics).

In my research, I look at the age pattern of mortality jumps, that is, how the effect of a mortality jump is distributed among different ages.

It is found that the age patterns of mortality jumps are not uniform over age and exhibit certain degrees of variation. These properties cannot be reflected in the traditional jump models that are based on aggregate mortality indexes.

Two jump models have been proposed to address the above issue.

Moreover, we found that the age pattern of jump effects has a huge impact on the pricing of catastrophic mortality bonds.
Description
Illustration

Model J0: jump effects and general period effects have identical age pattern (solid line).

Model J2: jump effects (red dotted line) and general period effects (blue dashed line) have different age patterns.
Illustration
MODEL WITH JUMP EFFECTS
MODEL WITH JUMP EFFECTS
Related Paper

Liu, Y. and Li, J.S.H., 2015. The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds. Insurance: Mathematics and Economics 64: 135150.
Related Paper
MortalityLinked Security Pricing

The method of canonical valuation is a fully nonparametric pricing method introduced by Stutzer (1996). The approach we consider is a semiparametric variant (Li, 2010; Chen et al., 2013a).

The canonical valuation method is very useful in retrieving the riskneutral probabilities from the market data, which can then be used in the pricing of mortalitylinked securities.

Alternative methods include the Wang transform (e.g., Chen and Cox, 2009) and the Esscher transform (e.g., Chuang and Brockett, 2014).
Description
Description
CANONICAL VALUATION
CANONICAL VALUATION
Related Paper

Liu, Y. and Li, J.S.H., 2015. The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds. Insurance: Mathematics and Economics 64: 135150.

Liu, Y., Li, J.S.H. and Ng, A.C.Y., 2015. Option pricing under GARCH models with Hansen's skewedt distributed innovations. North American Journal of Economics and Finance 31: 108125.
Related Paper
Mortality/Longevity Risk Measurement & Management

The traditional "delta" or "deltanuga" hedging methods aim to reduce the hedger's exposure to diffusion and drift risks.

They are subject to a few limitations, including the constraints on linearity and liquidity.


The generalized state space (GSS) hedging method overcomes the issues on linearity and liquidity.

The GSS hedging method is based on variance minimization.

The GSS hedging method can be used as long as the underlying model has a state space representation.

In comparison to the traditional delta and delta–nuga methods, the GSS method is more flexible in terms of the number and type of hedging instruments.

Under certain conditions, the GSS hedging method degenerates to the traditional delta and delta–nuga hedging methods.

Description
Description
Related Paper

Liu, Y. and Li, J.S.H., 2017. The locallylinear CairnsBlakeDowd model: A note on deltanuga hedging of longevity risk. ASTIN Bulletin 47: 79151.
Related Paper
GSS HEDGING METHOD
GSS HEDGING METHOD

Hedging with indexbased mortality derivatives gives rise to population basis risk. More specifically, population basis risk arises from the mismatch in mortality experience between (i) the population associated with the hedger and (ii) the population associated with the index used for hedging purposes.

In my research, I have derived an analytical decomposition of the hedge portfolio variance, through which population basis risk can be measured and managed explicitly.
Description
Description
Related Paper

Liu, Y. and Li, J.S.H., 2016. It's all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk. Insurance: Mathematics and Economics 70: 301319.
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COHORT EFFECT
COHORT EFFECT

Cohort (yearofbirth) effect, describes the variations in mortality experience for individuals born in different years.

Existing indexbased hedging strategies mitigate risks associated with period effects, but often overlook cohort effects.

In my research, I study how standardized qforwards can be used to mitigate risks associated with both period and cohort effects.

The hedging strategy can be derived through variance minimization or ValueatRisk minimization.
Description
Description
Related Paper

Liu, Y. and Li, J.S.H., 2018. A strategy for hedging risks associated with period and cohort effects using qforwards. Insurance: Mathematics and Economics, 78: 267285.