필사 모드: Life Insurance Actuarial Models & Variable Annuity 2026 Deep Dive: Lee-Carter, CBD, GMxB, K-ICS, IFRS 17 in One Place
EnglishThree Big Shifts Reshaping Life Insurance in 2026
In 2026 the life insurance industry is being reshaped by three forces. First, three years after IFRS 17 (Insurance Contracts) went live in both Korea and Japan in 2023, year-end close and EV reporting are fundamentally rewired. Second, Korea's Financial Services Commission launched the Korean Insurance Capital Standard (K-ICS) phase 1 in 2024 and phase 2 in 2026, and Japan's FSA started phased adoption of the IAIS Insurance Capital Standard (ICS) 2.0 from 2025. Third, COVID-19 disrupted the long-run mortality improvement trend, forcing fresh calibration of classical models such as Lee-Carter and Cairns-Blake-Dowd (CBD). This article walks actuaries, finance, risk and product teams through the models, capital regimes, hedging and product realities you must understand in 2026.
Survival Function and Mortality Rates: The Basic Math Revisited
The starting point of life actuarial science is the survivor count `l_x` and the mortality rate `q_x`. `l_x` is the number of people from a notional 100,000 cohort still alive at age `x`, and `q_x` is the probability that a person aged `x` dies within a year. The two are always linked by `l_{x+1} = l_x \cdot (1 - q_x)`. In continuous time we use the force of mortality `\mu_x` and write `l_x = l_0 \exp(-\int_0^x \mu_t dt)`. Korean KMT 2021, Japanese JMT 2018 and the US SOA RP-2014/MP-2021 experience tables all expose these two quantities.
Why Mortality Improvement Is the Decisive Variable
Annuities, whole life and variable annuities all carry longevity risk and are highly sensitive to the assumption that mortality improves a fixed amount each year. The SOA Retirement Plans Experience Committee (RPEC) followed RP-2014 with the MP-2014, MP-2017 and MP-2021 improvement scales. Korea's KIRI publishes mortality improvement rates every year. Excess COVID-19 mortality from 2020-2022 broke the trend, and as of 2026 both countries are working on Bayesian re-estimations that try to fold the COVID-19 effect into the long run trend.
Lee-Carter: The Classic Mortality Time Series Model
Lee and Carter's 1992 JASA paper decomposes log mortality as `log m_{x,t} = a_x + b_x \cdot k_t + e_{x,t}`. Here `a_x` is the average log mortality at age `x`, `b_x` is the age sensitivity, and `k_t` is a time index. SVD recovers `b_x` and `k_t`, and `k_t` is then extrapolated with an ARIMA model (typically random walk with drift) to forecast future mortality.
lee_carter.py — numpy/pandas implementation (compact)
def fit_lee_carter(mxt: pd.DataFrame):
"""
mxt: rows=age (x), cols=year (t), values=central mortality m_{x,t}
returns: a_x, b_x, k_t with sum(b_x)=1 and sum(k_t)=0
"""
log_m = np.log(mxt.values + 1e-12)
a_x = log_m.mean(axis=1)
Z = log_m - a_x[:, None]
U, S, Vt = np.linalg.svd(Z, full_matrices=False)
b_x = U[:, 0]
k_t = S[0] * Vt[0, :]
normalize
norm = b_x.sum()
b_x = b_x / norm
k_t = k_t * norm
k_t = k_t - k_t.mean()
return (
pd.Series(a_x, index=mxt.index, name='a_x'),
pd.Series(b_x, index=mxt.index, name='b_x'),
pd.Series(k_t, index=mxt.columns, name='k_t'),
)
def forecast_k(k_t: pd.Series, horizon: int = 30):
"""
Forecast k_t as a random walk with drift.
In production prefer statsmodels ARIMA(0,1,0)+drift.
"""
drift = (k_t.iloc[-1] - k_t.iloc[0]) / (len(k_t) - 1)
future_t = np.arange(1, horizon + 1)
return pd.Series(
k_t.iloc[-1] + drift * future_t,
index=range(int(k_t.index[-1]) + 1, int(k_t.index[-1]) + 1 + horizon),
name='k_t_hat',
)
Usage: download mxt from KOSIS or HMD, feed it to fit_lee_carter.
Lee-Carter is elegantly simple but has one major flaw: it forces every age to move with the same `k_t`, so cohort effects are hard to express.
Cairns-Blake-Dowd (CBD): Optimised for Older Ages
The CBD model proposed by Cairns, Blake and Dowd in 2006 is a logit-style model designed for older ages (60+). It writes `logit\,q_{x,t} = k_t^{(1)} + (x - \bar{x}) \cdot k_t^{(2)} + e_{x,t}` and models the two series `k^{(1)}` (level) and `k^{(2)}` (age slope) as a multivariate random walk. It is also called the M5 model, with M6 (cohort), M7 (quadratic) and M8 (flattening) as standard extensions.
cbd_m5.py — CBD M5 estimation
from scipy.special import logit
def fit_cbd_m5(qxt: pd.DataFrame):
"""
qxt: rows=age (60-89 recommended), cols=year, values=q_{x,t}
returns: k1_t, k2_t
"""
ages = qxt.index.values.astype(float)
x_bar = ages.mean()
Y = logit(qxt.values) # shape (n_ages, n_years)
X = np.column_stack([np.ones_like(ages), ages - x_bar]) # (n_ages, 2)
per-year OLS: Y[:, t] = X @ [k1_t, k2_t]
XtX_inv = np.linalg.inv(X.T @ X)
K = XtX_inv @ X.T @ Y # shape (2, n_years)
return (
pd.Series(K[0], index=qxt.columns, name='k1_t'),
pd.Series(K[1], index=qxt.columns, name='k2_t'),
)
def simulate_cbd_paths(k1: pd.Series, k2: pd.Series, n_sims: int, horizon: int, seed: int = 7):
rng = np.random.default_rng(seed)
dk1 = np.diff(k1.values)
dk2 = np.diff(k2.values)
mu = np.array([dk1.mean(), dk2.mean()])
cov = np.cov(np.vstack([dk1, dk2]))
paths = np.zeros((n_sims, horizon, 2))
start = np.array([k1.iloc[-1], k2.iloc[-1]])
for s in range(n_sims):
eps = rng.multivariate_normal(mu, cov, size=horizon)
paths[s] = start + np.cumsum(eps, axis=0)
return paths # shape (n_sims, horizon, 2)
CBD has less statistical drift than Lee-Carter and fits older ages better, which is why the IAA and OECD recommend it for pension valuation.
Heligman-Pollard: A Classic Single-Year Mortality Curve
The Heligman-Pollard 8-parameter model from 1980 decomposes a single year `q_x` into three components: infant mortality, the accident hump for young adults, and the exponential rise of old age. It takes the form `q_x / p_x = A^{(x+B)^C} + D \cdot \exp(-E (\log x - \log F)^2) + G H^x`. It is widely used when smoothing K-EX (Korean experience) or JLT (Japanese life table) curves, typically fit by nonlinear least squares with scipy.optimize.curve_fit.
Heligman-Pollard Fitting Code
heligman_pollard.py
from scipy.optimize import curve_fit
def hp8(x, A, B, C, D, E, F, G, H):
term1 = A ** ((x + B) ** C)
term2 = D * np.exp(-E * (np.log(x + 1e-9) - np.log(F)) ** 2)
term3 = (G * H ** x) / (1 + G * H ** x)
return term1 + term2 + term3
def fit_hp(ages: np.ndarray, qx: np.ndarray):
p0 = [0.0005, 0.02, 0.1, 0.001, 8.0, 22.0, 5e-5, 1.1]
bounds = (
[1e-6, 0, 0, 0, 0, 10, 1e-8, 1.0],
[1e-2, 1, 1, 1e-1, 30, 40, 1e-2, 1.2],
)
popt, pcov = curve_fit(hp8, ages, qx, p0=p0, bounds=bounds, maxfev=20000)
return dict(zip(list('ABCDEFGH'), popt)), pcov
Premium Pricing Basics: Single-Premium Whole Life and Term
Classical actuarial pricing writes the single net premium for a unit death benefit as `A_x = \sum_{k=0}^{\omega - x - 1} v^{k+1} \cdot _kp_x \cdot q_{x+k}`, where `v = 1/(1+i)` is the discount factor and `_kp_x` is the `k`-year survival probability. Whole life sums to `\omega - x`, term life only to n. The statutory valuation rate in both Korea and Japan fell from above 3% in the 2010s to under 1%, and has now recovered to around 2% as of 2024-26.
Reserves: FAS 60/97/120 vs IFRS 17 — The Fundamental Difference
US GAAP applies different accounting rules by product: FAS 60 (traditional whole life and term), FAS 97 (universal and variable life), FAS 120 (participating whole life). IFRS 17 unifies all insurance contracts under three measurement approaches: the General Measurement Model (GMM), the Variable Fee Approach (VFA) and the Premium Allocation Approach (PAA). The key change is that the Building Block Approach explicitly separates the three blocks of fulfilment cash flows—Best Estimate Liability (BEL) + Risk Adjustment (RA)—from the Contractual Service Margin (CSM).
What the IFRS 17 Contractual Service Margin (CSM) Means
The CSM is a liability that defers the unearned profit on an insurance contract so it can be recognised evenly across the coverage period. Profit no longer hits day one; it builds in the CSM and is then released each year in proportion to coverage units. Korea's big three life insurers—Samsung Life, Hanwha Life, Kyobo Life—shifted to IFRS 17 from year-end 2023 and now disclose their CSM balance as a leading indicator of operating profit.
ifrs17_csm_release.py — simplified CSM release simulation
def csm_release(initial_csm: float, coverage_units: np.ndarray, discount_rate: float):
"""
initial_csm: CSM balance at contract inception
coverage_units: coverage units by year (e.g. sum insured)
discount_rate: locked-in discount rate per IFRS 17 B72
"""
n = len(coverage_units)
csm_balance = np.zeros(n + 1)
csm_balance[0] = initial_csm
release = np.zeros(n)
for t in range(n):
accrued = csm_balance[t] * (1 + discount_rate)
remaining_cu = coverage_units[t:].sum()
rel = accrued * (coverage_units[t] / remaining_cu)
release[t] = rel
csm_balance[t + 1] = accrued - rel
return release, csm_balance
Use: release[t] is the profit recognised as insurance service result in year t.
What a Variable Annuity (VA) Actually Is
A variable annuity invests part of the premium in a fund pool, and the death benefit and surrender value vary with fund performance. Korea introduced VAs in the late 1990s and variable universal life exploded in the early 2000s. Japan built a major market in foreign-currency variable annuities (whole life and annuities) in the early 2000s. The funds are held in a separate account that is insulated from the insurer's general account.
GMxB: Guarantee Types and Their Nature
The heart of a VA is the GMxB guarantee. The family includes GMDB (death benefit), GMAB (accumulation), GMIB (income), GMWB (withdrawal) and GMMB (maturity). The policyholder is guaranteed at least principal back, or a guaranteed withdrawal, even when markets crash. Economically this is the insurer writing a long-dated put option. The 2008 crisis of AIG Financial Products Group's VA book was the result of failing to dynamically hedge that put.
Hedging GMxB: Greek-Based Dynamic Hedging
VA guarantees are essentially long-dated puts, so insurers measure Black-Scholes Greeks daily—delta (equity), vega (volatility), rho (rates), gamma (delta convexity)—and trade hedge assets (equity futures, variance swaps, rates swaps). Samsung, Hanwha and Kyobo in Korea, and Dai-ichi, Meiji Yasuda, Sumitomo and Tokio Marine Nichido Anshin in Japan all run dedicated ALM and hedging desks.
va_gmdb_delta.py — GMDB delta approximation
from scipy.stats import norm
def gmdb_pv_and_delta(
s0: float, k: float, r: float, q: float, sigma: float,
t_years: float, mortality_prob: float
):
"""
Highly simplified: approximate a GMDB as a T-year put option
times the mortality probability for the expected payout PV.
Production GMDB needs the integral of puts weighted by time of death.
"""
d1 = (np.log(s0 / k) + (r - q + 0.5 * sigma ** 2) * t_years) / (sigma * np.sqrt(t_years))
d2 = d1 - sigma * np.sqrt(t_years)
put = k * np.exp(-r * t_years) * norm.cdf(-d2) - s0 * np.exp(-q * t_years) * norm.cdf(-d1)
delta_put = -np.exp(-q * t_years) * norm.cdf(-d1)
pv = put * mortality_prob
delta = delta_put * mortality_prob
return pv, delta
AIG 2008: When a VA Book Nearly Took a Company Down
AIG aggressively sold GMDB and GMIB riders in the early 2000s, building a deep put-option liability. When markets cratered in 2008 the liability exploded, layered on top of CDS and MBS losses from the same group, and turned into a full-blown liquidity crisis. The Federal Reserve stepped in with an USD 85 billion emergency loan. The lessons are twofold. First, VA guarantees are long-dated, deep OTM puts, so they generate large hedging error compared to vanilla options. Second, statistical mortality assumptions and market risk have to be measured separately.
EIA (Equity-Indexed Annuity): Big in the US, Variable Universal in Korea
The Equity-Indexed Annuity caps and floors index returns (typically S&P 500) and credits the result to the accumulation. Insurers fund this by holding bonds plus a call option. Korea does not really sell pure EIAs but offers similar exposure through index funds inside variable universal life. In the US, Registered Index-Linked Annuities (RILAs) exploded in growth from the late 2020s.
The Revival of Japanese VAs: Foreign Currency and Trust Type
The Japanese VA market collapsed after the Nikkei crash in the late 1990s, then revived from the late 2010s through foreign-currency products denominated in US and Australian dollars. Dai-ichi Frontier, MetLife and AIG Salomon are the major distributors. In 2026, under persistently low rates and a weak yen, foreign-currency variable annuities are a core option for retiree wealth. However, currency volatility, surrender charges and complexity led Japan's FSA to tighten sales suitability guidance from 2023.
Mis-selling of Variable Annuities in Korea
In Korea the early 2010s saw a wave of mis-selling around variable universal life. Many policyholders signed up without grasping fund fees or surrender values. The FSS reinforced sales suitability rules in 2018 and made explicit disclosure of expense loadings mandatory after IFRS 17 adoption in 2023. As of 2026, new variable annuity sales have recovered but average ticket size is lower and the average age of buyers is younger than the previous cycle.
EV (Embedded Value) and VIF: The Standard Valuation Toolkit
EV = ANW (adjusted net worth) + VIF (value of in-force). VIF is the present value of post-tax cash flows from existing contracts. The CFO Forum's MCEV (Market Consistent Embedded Value) principles are the global standard, and Korea's big three plus Japan's majors publish EV reports annually. Since IFRS 17 went live, the relationship between CSM and EV has become a live topic—CSM is an accounting future-profit liability, VIF is an economic value, and the two do not exactly reconcile.
Solvency II: The European Original of Capital Regulation
Solvency II is the EU's insurance capital regime that took effect in 2016. It has three pillars: Pillar 1 (quantitative capital), Pillar 2 (governance and ORSA), Pillar 3 (disclosure). Pillar 1 computes a 99.5% VaR-based Solvency Capital Requirement (SCR), and own funds must exceed it. Risks—market, insurance, operational, counterparty—are computed in modules and combined with a correlation matrix.
K-ICS: The Structure of Korea's New Solvency Regime
Korea's K-ICS was rolled out in two phases—phase 1 in 2024 and phase 2 in 2026. The solvency ratio is available capital divided by required capital and must be at least 100%. Like Solvency II it uses 99.5% VaR over a one-year horizon and applies market, insurance, operational, credit and concentration risk modules. Unlike Solvency II, the insurance risk module is more granular to reflect Korea's heavier weighting in variable and universal products. As of end-2025 the market average is around 200% for Samsung Life, ~200% for Hanwha and Kyobo, and around 150% for mid- and small-sized insurers.
ICS 2.0: The IAIS Group Capital Standard
The IAIS Insurance Capital Standard (ICS) 2.0 applies to Internationally Active Insurance Groups (IAIGs). After a five-year monitoring period it became fully effective in 2025, with Japan, Canada and Australia among the early adopters. Korea is still an observer but is aligning K-ICS with ICS in tandem with IFRS 17.
Solvency II vs K-ICS vs ICS Side-by-Side Table
| Item | Solvency II | K-ICS | ICS 2.0 |
|---|---|---|---|
| Effective | 2016 EU | 2024 (P1) / 2026 (P2) KR | 2025 IAIS |
| Confidence | 99.5% VaR | 99.5% VaR | 99.5% VaR |
| Horizon | 1 year | 1 year | 1 year |
| Group vs Solo | Solo + Group | Solo-centric | Group-only |
| Valuation | Market-consistent | Market-consistent | Market-consistent (MAV) |
| VA treatment | VFA-like | Separate account + guarantee risk | VFA-aligned |
| Discount adj. | UFR + VA + MA | UFR + Korea-specific | OCIR |
Korean and Japanese Mortality Tables vs SOA: KMT, JMT, SOA
KIDI (Korean Insurance Development Institute) published KMT 2021 as the latest Korean experience table. Japan's actuaries (JILA) use JMT 2018. In the US, the SOA publishes RP-2014/MP-2021 for pensions. In general Japan has the longest life expectancy, then Korea, then the US. OECD averages in 2026 are about 80 for men and 86 for women; Korea sits at roughly 81.4 and 87.5, Japan at 81.6 and 88.0.
ILS and Longevity Bonds
Insurance-Linked Securities (ILS) transfer insurance risk into capital markets. CAT bonds (natural catastrophes) dominate; longevity bonds remain a small but growing slice that the OECD and G20 are pushing to standardise. Swiss Re Kortis Capital issued the first listed longevity bond in 2010, and reinsurers like SCOR, RGA and Munich Re now run an active longevity-swap business. Dai-ichi Life signed a longevity swap with a UK pension fund in 2023, attracting attention.
Life Settlement: The US Secondary Market
The US life settlement market—where policyholders sell their policies to third parties for cash—has grown to roughly USD 20 billion. The seller gets immediate cash, the buyer collects the eventual death benefit. Korea and Japan restrict this market legally, but SOA research notes that life settlement has become a real option in US senior wealth management.
The 2026 Actuarial Toolkit
The toolset actuaries and risk desks reach for in 2026 is roughly: (1) Python (pandas, numpy, scipy, statsmodels, PyMC), (2) R (lifecontingencies, demography, StMoMo, fmsb), (3) MATLAB/SAS (legacy), (4) commercial actuarial platforms such as Prophet, MoSes, AXIS. For K-ICS and IFRS 17 close, Moody's RiskIntegrity, Milliman MG-ALFA and Conning ADVISE lead the market. Korean and Japanese insurers run in-house simulation engines alongside these.
Common Anti-Patterns and Better Practice
The most common anti-patterns are: (1) using a single mortality table without applying an improvement scale, (2) leaving VA guarantees in static hedge, (3) failing to disclose assumption changes in EV reports, (4) presenting IFRS 17 CSM as if it were operating profit. Better practice involves: (1) running multiple scenarios (base, stress, COVID) in parallel, (2) twin controls of Greek limits plus scenario limits, (3) standardised assumption-change disclosure, (4) explicit decomposition of CSM, VIF and FX in disclosures.
Conclusion: Actuarial Science Is Again About Code and Capital
In 2026 life insurance actuarial science is no longer about table lookups. The standard is to fit Lee-Carter, CBD and HP yourself, hedge GMxB daily, and automate the K-ICS and IFRS 17 close. Major Korean and Japanese insurers run their actuarial-science and risk-IT teams as one unit and build their own Python and R platforms on top. Asset management, reinsurance, hedging and capital—four axes—now all sit on top of code.
References
- Society of Actuaries (SOA): https://www.soa.org/
- SOA RP-2014 / MP-2021 Mortality Improvement Scale: https://www.soa.org/resources/experience-studies/2021/mortality-improvement-scale-mp-2021/
- Casualty Actuarial Society (CAS): https://www.casact.org/
- International Actuarial Association (IAA): https://www.actuaries.org/
- KIRI (Korea Insurance Research Institute): https://www.kiri.or.kr/
- KIDI (Korea Insurance Development Institute): https://www.kidi.or.kr/
- FSC Korea K-ICS resources: https://www.fsc.go.kr/
- JILA (Japan Institute of Actuaries): https://www.actuaries.jp/
- Japan FSA insurance and ICS: https://www.fsa.go.jp/
- EIOPA Solvency II: https://www.eiopa.europa.eu/
- IAIS Insurance Capital Standard: https://www.iaisweb.org/
- IFRS 17 official: https://www.ifrs.org/issued-standards/list-of-standards/ifrs-17-insurance-contracts/
- Lee & Carter 1992 JASA paper: https://www.demog.berkeley.edu/~rlee/papers/Lee-Carter1992.pdf
- Cairns-Blake-Dowd 2006 reference: https://www.actuaries.org.uk/
- Human Mortality Database (HMD): https://www.mortality.org/
- StMoMo R package: https://cran.r-project.org/web/packages/StMoMo/
- CFO Forum MCEV Principles: https://www.cfoforum.eu/
- Milliman MG-ALFA: https://www.milliman.com/en/products/mg-alfa
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In 2026 the life insurance industry is being reshaped by three forces. First, three years after IFRS...