Fair Pricing of Variable Annuities with Guarantees under the Benchmark Approach

A Discrete Time Benchmark Approach for Insurance and Finance

Astin Bulletin ◽

10.1017/s0515036100013416 ◽

2003 ◽

Vol 33 (2) ◽

pp. 153-172 ◽

Cited By ~ 7

Author(s):

Hans Bühlmann ◽

Eckhard Platen

Keyword(s):

Discrete Time ◽

Jel Classification ◽

Optimal Portfolio ◽

Contingent Claim ◽

Fair Price ◽

Growth Optimal Portfolio ◽

Fair Pricing ◽

Pricing Rule ◽

Benchmark Approach ◽

Secondary 60G30

This paper proposes a consistent approach to discrete time valuation in insurance and finance. This approach uses the growth optimal portfolio as reference unit or benchmark. When used as benchmark, it is shown that all benchmarked price processes are supermartingales. Benchmarked fair price processes are characterized as martingales. No measure transformation is needed for the fair pricing of insurance policies and derivatives. The standard actuarial pricing rule is obtained as a particular case of fair pricing when the contingent claim is independent from the growth optimal portfolio.1991 Mathematics Subject Classification: primary 90A12 secondary 60G30, 62P20JEL Classification: G10, G13

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LESS-EXPENSIVE VALUATION AND RESERVING OF LONG-DATED VARIABLE ANNUITIES WHEN INTEREST RATES AND MORTALITY RATES ARE STOCHASTIC

Astin Bulletin ◽

10.1017/asb.2020.7 ◽

2020 ◽

Vol 50 (2) ◽

pp. 381-417

Author(s):

Kevin Fergusson

Keyword(s):

Interest Rates ◽

Mortality Rates ◽

Bessel Process ◽

Insurance Markets ◽

Rate Model ◽

Ancillary Benefits ◽

Variable Annuities ◽

Mortality Model ◽

Squared Bessel Process ◽

Benchmark Approach

AbstractVariable annuities are products offered by pension funds and life offices that provide periodic future payments to the investor and often have ancillary benefits that guarantee survival benefits or sums insured on death. This paper extends the benchmark approach to value and hedge long-dated variable annuities using a combination of cash, bonds and equities under a variety of market models, allowing for dependence between financial and insurance markets. Under a simplified case of independence, the results show that when the discounted index is modelled as a time-transformed squared Bessel process, less-expensive valuation and reserving is achieved regardless of the short rate model or the mortality model.

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A Discrete Time Benchmark Approach for Insurance and Finance

Astin Bulletin ◽

10.2143/ast.33.2.503688 ◽

2003 ◽

Vol 33 (02) ◽

pp. 153-172 ◽

Cited By ~ 10

Author(s):

Hans Bühlmann ◽

Eckhard Platen

Keyword(s):

Discrete Time ◽

Jel Classification ◽

Optimal Portfolio ◽

Contingent Claim ◽

Fair Price ◽

Growth Optimal Portfolio ◽

Fair Pricing ◽

Pricing Rule ◽

Benchmark Approach ◽

Secondary 60G30

This paper proposes a consistent approach to discrete time valuation in insurance and finance. This approach uses the growth optimal portfolio as reference unit or benchmark. When used as benchmark, it is shown that all benchmarked price processes are supermartingales. Benchmarked fair price processes are characterized as martingales. No measure transformation is needed for the fair pricing of insurance policies and derivatives. The standard actuarial pricing rule is obtained as a particular case of fair pricing when the contingent claim is independent from the growth optimal portfolio. 1991 Mathematics Subject Classification: primary 90A12 secondary 60G30, 62P20 JEL Classification: G10, G13

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