MSc.MF Theses and Dissertations (2022)

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Browsing MSc.MF Theses and Dissertations (2022) by Author "Mau, Erick Omondi"

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    Mathematical modeling of house price dynamics and their impact on the cost of No Negative Equity Guarantee: evidence from Kenya
    (Strathmore University, 2022) Mau, Erick Omondi
    Equity Release Mortgages (ERMs) are significantly required in an aging population with high homeownership levels. The capacity to identify the risks associated with the cost of the No Negative Equity Guarantee is an essential aspect of a risk management tool for most annuity and pension providers. Therefore, the main objective of this research is to; institute a stochastic modeling framework for the No Negative Equity Guarantee (NNEG) in an Equity Release Mortgage (ERMs) loan, and the payoff structure of the NNEG, and finally price the Equity Release Mortgages. An ARMA-EGARCH model that can capture auto-correlation and volatility clustering characteristics is proposed based on the model fittings. To analyze the regional and the national effect, we evaluate different models using the bench-marked loan data obtained from the nationwide building society database in the United Kingdom, for the period between 1991-2020 and had details such as the amount borrowed, age, marital status, and sex among others during the period. House Price Index (HPI) data was used to calibrate the loan data. Four baseline scenarios were used to simulate the NNEG valuation: the loan-to-value ratio, the roll-up rate, the risk-free rate, and house price volatility. The model forecasting power was evaluated using: root means squared errors, mean average error, the Diebold-Mariano forest accuracy test, and Occam's razor method. However, due to fluctuations in the house price data-generating process and goodness of fit, the Diebold-Mariano forest accuracy test was used as the metric to evaluate the model's performance in providing superior forecasting power. The study adopts the suggestion of (Hosty et al., 2008) to investigate the model risk on the cost of NNEGs and further develops a risk-neutral valuation methodology using the Conditional Esscher Transform Technique as proposed by (Buhlmann et al., 1996). The findings indicate that ARMA (4, 3)-EGARCH (1, 1) outperformed both the Black (1976) and the Geometric Brownian Motion-risk-neutral (GBM-rn) with a score of 0.2637. The simulation results further established that the cost of NNEG is critically sensitive and robust to; the Roll-up rate, Loan-to-Value (LTV) ratio, the volatility of the house prices, the risk-free rate, and the rental yield. Also, under current market settings, the Geometric Brownian Motion (GBM)-rn and Black' 76 may suddenly increase the NNEGs values via higher than obligatory volatilities at longer time horizons.