Hedging Costs for Variable Annuities Under Regime-Switching

This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

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LOCAL HEDGING OF VARIABLE ANNUITIES IN THE PRESENCE OF BASIS RISK

Astin Bulletin ◽

10.1017/asb.2018.7 ◽

2018 ◽

Vol 48 (02) ◽

pp. 611-646 ◽

Cited By ~ 7

Author(s):

Denis-Alexandre Trottier ◽

Frédéric Godin ◽

Emmanuel Hamel

Keyword(s):

Regime Switching ◽

Value At Risk ◽

Capital Requirements ◽

Optimization Criterion ◽

Local Optimization ◽

Conditional Value At Risk ◽

Variable Annuities ◽

Basis Risk ◽

Hedging Strategies ◽

Risk Metric

AbstractA method to hedge variable annuities in the presence of basis risk is developed. A regime-switching model is considered for the dynamics of market assets. The approach is based on a local optimization of risk and is therefore very tractable and flexible. The local optimization criterion is itself optimized to minimize capital requirements associated with the variable annuity policy, the latter being quantified by the Conditional Value-at-Risk (CVaR) risk metric. In comparison to benchmarks, our method is successful in simultaneously reducing capital requirements and increasing profitability. Indeed the proposed local hedging scheme benefits from a higher exposure to equity risk and from time diversification of risk to earn excess return and facilitate the accumulation of capital. A robust version of the hedging strategies addressing model risk and parameter uncertainty is also provided.

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On the Bayesian Risk Evaluation of Minimum Guarantees in Variable Annuities

Asia-Pacific Journal of Risk and Insurance ◽

10.1515/apjri-2015-0007 ◽

2015 ◽

Vol 0 (0) ◽

Author(s):

Byoung Hark Yoo ◽

Bangwon Ko ◽

Hyuk-Sung Kwon

Keyword(s):

Regime Switching ◽

Capital Requirements ◽

Variable Annuities ◽

Substantial Impact ◽

Statistical Framework ◽

Volatility Models ◽

Volatility Model ◽

Significant Difference ◽

Korean Market

AbstractLong-term equity return models have a substantial impact on calculating reserves and capital requirements for minimum guarantees in variable annuities (VAs). Under a Bayesian statistical framework, we reinvestigate the standard long-term equity return models (independent lognormal, regime-switching lognormal and stochastic log volatility models) with the Korean equity market data. Our empirical analysis shows that the long-term behaviors of the Korean market are best described by the regime-switching lognormal models, and there can be significant difference in the amount of the reserves and the capital requirements depending on the model selection. The long-term nature of the VA contracts requires that more caution be paid for modeling the mean part of the stochastic log volatility model.

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