Volatility Relations in Stocks, Dividends and Lifetime Income

The aim of this thesis is to investigate financial solutions for improving the quality of life for retired seniors. The main pillars of research are associated with equity release mortgages (ERMs) and dividend payments, as a cash-flow related solution which can boost pensioners income.This thesis investigates: i) international evidence of the dividend volatility puzzle with empirical focus on understanding dividend and stock price volatility issues in the present value relation by examining the variance bound inequality introduced by Shiller (1981) and Leroy (1981); ii) variance bound inequality by examining implied dividend volatility estimated from novel data emanating from index dividend future options and stock index options respectively. iii) pricing mechanism for non-negative equity guarantee (NNEG) clause in ERM contracts with detailed analysis on the model risk sensitivity, parameter estimate sensitivities, and borrower characteristics. iv) from a portfolio viewpoint, the joint dynamics of funding cost, long term effect of house price risk, and property impairment characterising NNEG valuation.Chapter 2 contributes to the emerging debate on stock-dividend volatility by providing a multi-national assessment on the long-run behaviour of dividend volatility within financial markets in developed economies. This was done vis-à-vis equity market volatility, utilising stock-index data spanning from 1800s to December 2018. An examination of Robert Shiller's stock-dividend volatility puzzle was conducted by replicating his argument within extended financial market data on the S\&P index spanning January 1871- December 2018. The purpose was to capture Shiller's procedure for forecasting long-run dividend growth and subsequently compare the performance of the replicated study under newly improved long-run regression-based methods. This allows for an examination of the consistency of the stock-dividend volatility puzzle across different market indices in various financial markets. The findings support the continuance of the puzzle; however, the magnitude of volatility violation showed a significant decrease over the long-run.Chapter 3 provides new evidence on the stock-dividend volatility puzzle by exploring implied volatilities on stock and dividend markets in novel financial derivative products. There was a comparison of information on the implied volatility surface of stock-index to the corresponding implied volatility surface of index dividend futures on the stock index. The thesis outlined a computational procedure for aggregating implied volatility estimates based on the Black-Scholes, Black model, and the model-free approach. Our findings illustrate how implied volatility term-structure of STOXX 50 with time-to-maturity exceeding 9-months moves enough to be justified by subsequent dividend fluctuations. Options with maturities between 1-9 months lead to implied volatilities that move too much to be justified by forward-looking changes in dividends. The implied volatility term structure of stock consistently exceeds that of index dividend futures thereby confirming Shiller's dividend puzzle under novel financial data and instruments. However, the magnitude of excess implied volatility declines with long-dated time-to-maturity, suggesting that discrepancies between the two are influenced by the investment horizon. Further, the thesis designed a set of trading strategies using implied volatility and the ratio of implied volatilities as a trading signal that proves to be successful for STOXX50 equity space.Chapter 4 focuses on understanding the issues associated with the pricing mechanisms for the non-negative equity guarantee (NNEG) clause in ERM contracts, taking a detailed look at model risk. More specifically, this chapter compared the NNEG valuation principles under the Black-Scholes model that is recommended by the regulations in the UK with a more academic approach based on time-series modelling for gauging the underlying house price risk. The chapter also investigates parameter sensitivities under both models and further determine the conditions under which the two models can produce similar outcomes. Our preliminary findings on NNEG valuation in both loan-by-loan and portfolio viewpoints show that the GBM model consistently overestimates the NNEG cost. The rental-yield parameter turns out to be the key risk driver in the NNEG valuation.Chapter 5 extends the context of the NNEG cost pricing study by investigating the fundamental effect of idiosyncratic or dilapidation risk of the collateral house in the ERM contracts. The chapter specifically investigates the characteristics of the NNEG values under the requisite and well-known empirical features of UK house price data that are often absent in perfectly rational models. The thesis focuses on the cash flow implications of the two models introduced and discussed in chapter 4. The final sections of the chapter are dedicated to analysing and parameterising property impairment that the loan issuer automatically inherits via the ERM loan contract. The model for the impairment to collateral house uses a value compressing factor that adjusts the market value of the underlying house prices for the impact of dereliction/dilapidation of property maintenance. This allows the loan issuer to isolate and analyse the resulting pool of impaired collateral properties. Shiller & Weiss (2000) attributes this potential reduction in property to lack of maintenance by the ERM borrower who may face a lessened financial interest in the collateral house. Modelling the impairment factor allows us to further investigate the issue of hefty discounting applied to home values as mentioned in Warshawsky & Zohrabyan (2016). The findings are indicative of a positive relationship between implied volatility and the impairment factor in ERM portfolios. Also, house price pathways under the GBM model display more variability compared to that of the ARMA-EGARCH model; thereby suggesting a higher likelihood for house prices to be overall lower at long term horizons. The loan issuer's earnings at risk are larger under the GBM model, leading to higher reserve liabilities for loan contracts. The time series model seems to provide an opportunity for the loan issuer to capture extreme tail observations in the earnings at risk, thereby allowing us to closely observe the longterm effect of collateral house price idiosyncratic risk.Chapter 6 outlines final discussions that conclude the thesis and point towards new directions in which this research might take to fill the existing gaps in the literature. The Appendices at the end of the thesis presents further results and materials which are separated from the main text.