• Journal of the Korea Society for Simulation
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• v.28 no.3
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• pp.57-63
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• 2019

This study suggests the level of guaranteed reserves that should be accumulated in order to provide guaranteed interest contracts to pension members. To calculate the guaranteed reserve, this study employs the method using variable insurance contracts with guaranteed interest options. The average return of three major pensions (national pension, private teacher's pension, civil servants pension) funds, from 2010 to 2018, is set as the target rate of return and then we establish 0%, 1.0%, 1.5% and 2.0% each as our minimum guaranteed returns for their respective guaranteed reserves. Our results firstly show that gaps between each guaranteed reserves are increasing as times goes on. Second, the probability of shortfall reserve is on the decrease as the pension fund is mature. Conclusively, a long-term conservative balance between risk and return is one of the best investing strategies in pension funds providing the guaranteed interest.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.249-264
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• 2009

Equity-indexed annuities(EIAs) provide their customers with the greater of either the return linked to the underlying index or the minimum guaranteed return. Insurance companies have developed EIAs to attract customers reluctant to buy traditional fixed annuities because of low returns and also reluctant to buy mutual funds for fear of the high volatility in the stock market. This paper proposes a new type of EIA embedded with an outside barrier option with flexible monitoring period in order to increase its participation rate. It also derives an explicit pricing formula for this proposed product, and discusses numerical examples to show relationships among participation rate, barrier level, index volatility and correlation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.83-96
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• 2011

This work proposes a binomial method for pricing the cliquet options, which provide a guaranteed minimum annual return. The proposed binomial tree algorithm simplifies the standard binomial approach, which is problematic for cliquet options in the computational point of view, or other recent methods, which may be of intricate algorithm or require pre- or post-processing computations. Our method is simple, efficient and reliable in a Black-Scholes framework with constant interest rates and volatilities.

• The Journal of the Korea Contents Association
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• v.20 no.11
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• pp.281-291
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• 2020

This study used Gauss-Poisson jump diffusion process on standard assets to estimate the statutory reserves of Variable Annuity (VA) guarantees specified in Korean bylaw of insurance supervision and calculated guarantee fees and risks based on the model to see the effect of considering the jumps. Financial assets, except KOSPI 200, have fat-tailed return distributions, which is an indirect evidence of discontinuous jumps. In the case of a domestic stock index and foreign stock indexes(Korean Won), guarantee fees and risks decrease when jumps are considered in models of underlying assets. This is explained by decreases in standard deviations after the jump diffusion is considered. On the other hand, in the case of domestic bond indexes and a foreign bond index(Korean Won), guarantee fees and risks tend to increase when jumps are considered. Results from a foreign stock index(US Dollar) and a foreign bond index(US Dollar) were opposite to those from the same kinds of Korean Won indexes. We conclude that VA guarantee fees and risks may be under or over estimated when jumps are not considered in models of underlying assets.