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Research Article Open access CC BY 4.0

Stochastic Modeling of Inflation and Interest Rates for Defined Benefit Pension Plan Projections in Ghana

Ravenhill Adjetey Laryea, Hanson Dela Quarshie, Ezekiel Nii Noye Nortey, Kwabena Doku-Amponsah

Journal of Advances in Mathematics and Computer Science · pp. 84–98 · Published 26 Dec 2022

10.9734/jamcs/2022/v37i121731

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.

Pension pension cost methods stochastic modelling normal cost actuarial liability

References (8)

  1. 1 Time Series Analysis: Forecasting and Control [DOI]
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