Stochastic Modeling of Inflation and Interest Rates for Defined Benefit Pension Plan Projections in Ghana
Ravenhill Adjetey Laryea *
Department of Banking and Finance, University of Professional Studies, Accra (UPSA), Ghana.
Hanson Dela Quarshie
Department of Statistics and Actuarial Science, School of Physical and Mathematical Sciences, College of Basic and Applied Sciences, University of Ghana, Box LG 115, Legon, Ghana.
Ezekiel Nii Noye Nortey *
Department of Statistics and Actuarial Science, School of Physical and Mathematical Sciences, College of Basic and Applied Sciences, University of Ghana, Box LG 115, Legon, Ghana.
Kwabena Doku-Amponsah
Department of Statistics and Actuarial Science, School of Physical and Mathematical Sciences, College of Basic and Applied Sciences, University of Ghana, Box LG 115, Legon, Ghana.
*Author to whom correspondence should be addressed.
Abstract
Aims/ Objectives: Pension plan administrators, employers and managers in exchange for service provided currently by employees’ pledges stated benefits in the prospective future. For this expense to be budgeted for the future, a pension cost method is used by the plan administrator to establish a form of warranty for the member. The aim of the study was to use deterministic pension plan projection but also considers economic variables that are stochastic, allowing the variables to change in the future randomly to model pension plan projections
Study Design: The study design was cross-sectional.
Data and Duration of Study: The data used were obtained from the Bank of Ghana as published on their official website. The sample data consists of three hundred and forty-eight (384) observations of monthly inflation rates in Ghana. It covers thirty-one (31) years period spanning from January 1990 to December 2021.
Methodology: Two methods were used to calculate the normal cost, that is, the total and projected unit credit cost using different interest rates and inflation assumptions and constant single life annuity. The economic variables inflation and interest rates were modeled based on data from the Bank of Ghana.
Results: Several time series models were considered, with the seasonal ARIMA (3,1,0)x(2,0,0)12 was the most appropriate time series model for inflation whereas was the best model for interest rate was the nonseasonal ARIMA(1,1,0). Based on the final models selected for the variables, 30 years ahead were forecasted, 100 stochastic simulations were generated on inflation and interest rate variables for the stochastic scenarios. Numerous economic scenarios were generated, 5th, 25th, 50th, 75th and 95th percentiles of probabilities associated with the values were obtained from the cost.
Conclusion: The study revealed that at age 59, the cost under the total unit cost of allocation method had a 0.05 probability of been less than 1.694 and a 0.95 probability that the cost would be lesser than 1.859 and under projected unit cost of allocation method, the cost had a 0.05 probability of been less than 37.284 while 0.95 probability of the cost been less than 45.408 at age 59.
Keywords: Pension, pension cost methods, stochastic modelling, normal cost, actuarial liability