Stochastic volatility models in financial econometrics: an application to South Africa

Malumisa, Sambulo
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The dissertation carries out a study to understand asset price behaviour in South Africa. This is investigated through the application of stochastic volatility models to trace the characteristics of high frequency financial data; daily temperature, exchange rates, interest rates, stock and house prices. Innovation in the derivatives market has seen the introduction of weather derivatives as a risk mitigation tool against adverse weather movements. Chapter Two applies three different time series models of temperature to estimate payoffs to determine which method offers the best hedging strategy in four South African cities. Results from the study suggest that the seasonality GARCH method of estimating payoffs for temperature based weather derivatives offers superior performance compared to the Cumulative Cooling Degree Days (CDD) and the historical method. This suggests that the seasonality GARCH method can be applied in these cities to hedge against adverse temperature movements. In Chapter three we consider the estimation methodology for jump diffusion models and GARCH models. Chapter four investigates volatility on exchange rate data. Use is made of the british pound/south african rand, euro/south african rand and u.s dollar/ south african rand exchange rates. The research introduces a jump diffusion model to trace the behaviour of exchange rate data. Estimation results are able to match the summary statistics in mean, variance, skewness and kurtosis. Results from the model can also explain the volatility smile for short and medium term maturities. A fat tailed GARCH model is introduced to capture the persistence in volatility on exchange rate data. Results from this chapter have an implication for pricing currency options to offer leverage to organisations affected by exchange rate risk. Chapter five extends the analysis to study the behaviour of short term interest rates, making use of the 90 Day Treasury bill (T-Bill) rate. The chapter considers a variant application of the Chan et al. (1992) model for short term interest rates wherein a jump diffusion model is introduced. The results match the summary statistics equivalent suggesting the capability of the model specification. Splitting the estimation period suggests that the jump size is highest post inflation target though with a smaller intensity. However, the 90 Day T-Bill shows higher volatility after inflation targeting though with a lesser intensity. These findings have a bearing on valuation of short term interest derivatives and also investigating multi factor models of interest rates. In chapter six four vi sectors (banking, mining, media and leisure) are considered to explore movements in stock prices. A jump diffusion model is applied to get estimation results. The results confirm related studies that stock prices have incidents of volatility which can be captured by a jump diffusion model. The results also shed light on the importance of portfolio diversification considering the different results across the sectors investigated. The implication also lies in understanding market efficiency. Chapter seven applies the jump diffusion model on house prices to understand more on the drivers of volatility on house prices. The interesting results on this chapter can be summarised as follows; the four different house segments have almost similar jump sizes though the small house price segment has highest intensity. This can point to expectations and volatility from participants in this segment at a higher level than for other segments over different regimes over the study period. The estimated higher moments were not normalised as had happened for the three previous chapters after introducing the jump diffusion model. Results from this chapter have an application to valuing mortgage premium across different house price segments. It is recommended that rigorous research on asset prices using various approaches be considered as it goes a long way in informing policy makers and investors to mitigate risk in an environment of volatile asset prices. With the growing interest in weather derivatives world-wide, there is a need to educate farmers, government entities, potential counter-parties and other organisations affected by weather related risk on the importance of weather derivatives so that a foundation is laid for trading in this special type of insurance.
Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Commerce, Law & Management, School of Economic and Business Sciences, 2015.