GUARANTEE VALUATION IN NOTIONAL DEFINED CONTRIBUTION PENSION SYSTEMS

2016 ◽  
Vol 46 (3) ◽  
pp. 677-707 ◽  
Author(s):  
Jennifer Alonso-García ◽  
Pierre Devolder
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Form Solution ◽  
Pension Scheme ◽  
Dependence Structure ◽  
Defined Contribution ◽  
Index Set ◽  
Notional Defined Contribution ◽  
Utility Indifference ◽  
Pension Adequacy

AbstractThe notional defined contribution pension scheme combines pay-as-you-go financing and a defined contribution pension formula. The return on contributions is based on an index set by law, such as the growth rate of GDP, average wages or contribution payments. The volatility of this return compromises the system's pension adequacy and therefore guarantees may be needed. Here, we provide a minimum return guarantee to the pension contributions. The price is calculated in a utility indifference framework. We obtain a closed-form solution for a general dependence structure with exponential preferences and in presence of stochastic short interest rates.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

scholarly journals The transition to NDC in Italy: assessing distributive and financial effects

2021 ◽  
pp. 1-16
Author(s):  
Carlo Mazzaferro
Keyword(s):  
Net Present Value ◽  
Pension System ◽  
Pension Scheme ◽  
Defined Benefit ◽  
Defined Contribution ◽  
Ratio Distribution ◽  
Actuarial Fairness ◽  
Notional Defined Contribution ◽  
High Level ◽  
Pension Benefits

Abstract Moving from a Defined Benefit (DB) to a Notional Defined Contribution (NDC) pension formula creates significant re-distributive effects. We estimate the amount and the intensity of these effects in the case of the Italian transition to NDC, which began in 1995. Based on administrative data of the main Italian pension scheme (FPLD), we study the evolution of yearly inequality within old-age pension benefits. Furthermore, we study the adequacy and the actuarial fairness of the pension system, by estimating the replacement rates and the Net Present Value Ratio distribution for workers who retired in the period 1996–2019. Our results show that the very generous interpretation of acquired rights determined by the 1995 reform has contributed to maintaining a high level of adequacy and a significant level of intergenerational imbalance. The financial costs of this imbalance are estimated and its extent is significant.

scholarly journals Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chubing Zhang
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Pension Funds ◽  
Form Solution ◽  
Defined Contribution ◽  
Time Dynamic ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

scholarly journals A GENERAL EQUILIBRIUM MODEL OF THE TERM STRUCTURE OF INTEREST RATES UNDER REGIME-SWITCHING RISK

2005 ◽  
Vol 08 (07) ◽  
pp. 839-869 ◽  
Author(s):  
SHU WU ◽  
YONG ZENG
Keyword(s):  
General Equilibrium ◽  
Interest Rates ◽  
Term Structure ◽  
Risk Premium ◽  
Equilibrium Model ◽  
Regime Switching ◽  
Yield Curve ◽  
Closed Form Solution ◽  
Form Solution ◽  
General Equilibrium Model

This paper develops a general equilibrium model of the term structure of interest rates in the presence of the systematic risk of regime shifts. The model elucidates the economic nature of the regime-shift risk premium and introduces a new source of time-variation in bond returns. A closed-form solution for the term structure of interest rates is obtained under an affine model using log-linear approximation. The model is estimated by Efficient Method of Moments. The regime-switching risk is found to be statistically significant and mostly affect the long-end of the yield curve.

scholarly journals Explicit Solution of the Optimal Reinsurance-Investment Problem with Promotion Budget

2016 ◽  
Vol 4 (2) ◽  
pp. 131-148
Author(s):  
Delei Sheng
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Hjb Equation ◽  
Form Solution ◽  
Control Technique ◽  
Insurance Company ◽  
Risk Management Process ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman ◽  
Policy Holder

AbstractThe lack of surrendering profits to policy holder leads to the development of this paper. For an insurer with promotion budget, both the interests of the insurance company and policy-holder are given a balance. In addition, promotion budget is introduced into the risk management process, which makes cheap reinsurance more fair. This article aims at obtaining the explicit strategy and value function for an investment-reinsurance problem under stochastic interest rates. Applying stochastic control technique, a Hamilton-Jacobi-Bellman (HJB) equation is established. The closed-form solution for the HJB equation and a verification theorem are obtained. At last, some numerical analysises illustrate the impacts of different parameters.

The Notional Defined Contribution Pension Scheme and the German ‘Point System’: A Comparison

2018 ◽  
Vol 19 (4) ◽  
pp. 365-382 ◽  
Author(s):  
Vera Gurtovaya ◽  
Sergio Nisticò
Keyword(s):  
Pension System ◽  
Pension Scheme ◽  
Point System ◽  
Defined Contribution ◽  
Rates Of Return ◽  
System A ◽  
Analytical Properties ◽  
Notional Defined Contribution

AbstractThis paper examines the analytical properties of the German ‘points-based’ pension system. These properties are compared with those of a canonical Notional Defined Contribution (NDC) pension scheme. The paper identifies the circumstances under which the German ‘points-based’ system would mimic a Swedish-type NDC scheme and verifies to what extent the German ‘points-based’ scheme ensures uniformity of individual rates of return for some hypothetical careers. Finally, the paper proposes a set of new possible adjustment rules able to increase similarity between the German point system and the NDC scheme.

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