Marriage Reverse Annuity Contract and Reverse Mortgage – Application of a Generalized Model of Reversionary Annuity

We model the probabilistic structure and cash flows arising from marriage reverse annuity contracts in the case of the joint-life status and the last surviving status. In contrast to the classical approach, we take into consideration that future lifetimes between spouses are dependent. The structure of dependence of the length of spouses' lives is modelled using copulas. The term structure of interest rate is modelled using a time-dependent function. The numerical results are based on actual Polish data covering both the structure of the probabilistic model and the interest rate.

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“…. For k = 1, 2, ..., n, the k-th discounting factor is given by the following formula (Lee et al, 2012;Marciniuk, 2017):…”

Section:  mentioning

confidence: 99%

Application of Copulas to Modelling of Marriage Reverse Annuity Contract

Dębicka¹,

Heilpern²,

Marciniuk³

2020

Prague Economic Papers

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“…When one partner dies, a fraction F is paid. Based on the Corollary (Marciniuk, 2017), the benefi t is calculated using the following formula:…”

Section: Market Value Of Property In Czechia Poland and Slovakiamentioning

confidence: 99%

“…The parameters of the function R 0,k can be estimated by least squares, using real market data, related to the yield to maturity on zero-coupon and fi xed-interest bonds for each country (Anderson et al, 1996;Marciniuk, 2017). As Slovakia belongs to the euro area, and moreover the Solvency II Directive (2009) requires the use of the European Central Bank's spot interest rates in certain insurance contracts, the best-fi tting model of spot interest for the euro area real data and the parameters of R 0,k was taken from the European Central Bank 1 .…”

Section: Market Value Of Property In Czechia Poland and Slovakiamentioning

confidence: 99%

“…In the sale model (home reversion scheme), the buyer exchanges the property for the promise of a certain sum at regular intervals, until the buyer dies. According to Dębicka and Marciniuk (2014), Marciniuk (2017), and Marciniuk and Zimková (2018), both products are available in Poland, although equity release is not yet as popular as it is in the USA or the UK.…”

Section: Introductionmentioning

confidence: 99%

“…These authors considered the dependence between spouses' future lifetimes. In Marciniuk (2017), the reverse annuity is applied to derive two lemmas used to determine marriage benefi ts payable more than once a year in the case of Last Surviving Status and Joint Life Status (when a reduction factor F = {0, 1}) for Polish voivodeship data. As many property owners are couples, the contracts need to specify what happens when one of the spouses dies.…”

Section: Introductionmentioning

confidence: 99%

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Valuation of Equity Release Contracts in Czech Republic, Republic of Poland and Slovak Republic

Marciniuk¹,

Zimková²,

Farkašovský³

et al. 2020

Prague Economic Papers

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An ageing European population and, therefore, a rising dependency ratio of retirees to the working population, strongly suggests that a pension funding gap will be a key social issue in future. Yet many older people have significant real estate assets that they could access using equity release products. They could sell their assets in exchange for lifelong or temporary monthly payments. Equity release products are relatively new to Poland, but are not yet offered by commercial banks in Czechia and Slovakia. This paper estimates the potential benefits of marriage reverse annuity, and reverse mortgage contracts, using the Svensson model function, and empirical property data from selected Czech, Slovak and Polish cities. The results are also compared to the average pension of inhabitants in the selected cities. It is shown that there is substantial scope for boosting retirement income in all the cases considered, though the precise size of the increase depends on factors such as contract buyers' age and life expectancy, the value of their assets, the payment consequences of a spouse's death, and contract suppliers' pricing policies.

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Modelling of lung cancer survival data for critical illness insurances

Dębicka

Zmyślona

2019

Stat Methods Appl

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We derive a general multiple state model for critical illness insurances. In contrast to the classical model, we take into account that the probability of death for a dread disease sufferer may depend on the duration of the disease, and the payment of benefits associated with a severe disease depends not only on the diagnosis but also on the disease stage. We apply the introduced model to the analysis of a critical illness insurance against the risk of lung cancer. Based on the real data for the Lower Silesian Voivodship in Poland, we estimate the transition matrix, related to the discrete-time Markov model. The obtained probabilistic structure of the model can be directly used to cost not only critical illness insurances and life insurances with accelerated death benefits option, but also to viatical settlement contracts.

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Marriage Reverse Annuity Contract and Reverse Mortgage – Application of a Generalized Model of Reversionary Annuity

Cited by 5 publications

References 2 publications

Application of Copulas to Modelling of Marriage Reverse Annuity Contract

Application of Copulas to Modelling of Marriage Reverse Annuity Contract

Valuation of Equity Release Contracts in Czech Republic, Republic of Poland and Slovak Republic

Modelling of lung cancer survival data for critical illness insurances

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