A Study on the Monthly Payments of the Farmland Reverse Mortgage System
Authors:   Asia-Europe Perspective Association, Noh Jinsu , Jang Woon Wook 
Published: June 2018

South Korea’s population is aging rapidly. Since becoming categorized as an ‘aging society’ in 2000, the elderly population in South Korea has increased at a dramatic pace, so much so that the country is expected to be categorized as an ‘aged society’ by 2018, and as a ‘super-aged society’ by 2026. The aging problem is particularly more serious in the rural areas. According to a 2013 study published by Statistics Korea, while the rate of aging for the entire population is 12.2%, the rate of aging for the farmer population is 37.3%, a rate that is high enough to speed up the move to a ‘super-aged society.’ In order to alleviate the aging problem and the related welfare problem of the elderly in the rural areas, the Korea government launched the Farmland Reverse Mortgage System (FRMS) in January 2011, a pension plan secured by farmland and is guaranteed by a federal agency, the Korea Rural Community Corporation (KRCC). The major risk factors for consideration in the management of the FRMS are farmland price risk, interest rate risk, and longevity risk. These risk factors are taken into consideration when the monthly payments are determined using the farmland collateral price, age of the pension holder, and the interest rate as the main variables.
In the current FRMS model, farmland prices are assumed to increase deterministically with a 2.85% rate of farmland price increase. In addition, the model applies a constant interest rate of 4% for the calculation of monthly payments, and uses the national mortality rate in the life table (women) published by the Statistics Korea in 2011. In this paper, we apply a more realistic model assumptions for each risk factor and study the appropriateness of the current FRMS monthly payments. Firstly, we applied a stochastically varying farmland price dynamics instead of the deterministic one used in the current FRMS model. Specifically, we model farmland price using geometric Brownian motion. Numerical analysis shows that, after reflecting for volatility risk in the farmland price dynamics, lower monthly price levels are calculated. Secondly, instead of the constant 4% interest rate used in the current FRMS model, we apply a 3-factor dynamic term structure model (DTSM) for the calculation of the monthly payments. We estimate the DTSM model parameters using the maximum likelyhood estimation (MLE) method. In the MLE we use weekly Korean Treasury Bonds and AAA bank bonds data (1, 2, 3,4, 5, 7, and 10 years maturity). Data periods cover the period from January 2002 to July 2014. In the application of the DTSM for the monthly payment calculations, we obtain higher monthly payment levels, which is a reflection of the low interest rate environment after the global financial crisis in 2008. Lastly, instead of using the national life table, we use the experience life table published by the Korea Insurance Development Institute, where longevity risk taken more into consideration. Application of the mortality rates given by the experience life table gives monthly payment levels that are comparatively lower than the current levels. When we apply all three assumptions into the model at the same time, we obtain monthly payment levels that are rather similar to the current levels. This result is driven by the existence of an offsetting effect between the decreasing factors (stochastic farmland price dynamics and the experience life table) and the increasing factor (stochastic interest rate model).
Empirical results of this paper show that the current level of FRMS monthly payments is within a reasonable range even after applying the more realistic assumptions for each of the risk factors within the reverse mortgage model. However, this should not be interpreted as evidence that the current FRMS model is sound as the result observed is driven by the offsetting effect between the risk factors.