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This thesis studies the impacts of credit risk, or the risk of default, on the pricing of fixed income securities. It consists of three essays. The first essay extends the classical corporate debt pricing model in Merton (1974) to incorporate stochastic volatility (SV) in the underlying firm asset value and derive a closed-form solution for the price of corporate bond. Simulation results show that the SV specification for firm asset value greatly increases the resulting credit spread levels. Therefore, the SV model addresses one major deficiency of the Merton-type models: namely, at short maturities the Merton model is unable to generate credit spreads high enough to be compatible with those observed in the market. In the second essay, we develop a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. Our empirical results show that the model is successful at fitting actual corporate bond credit spreads. In addition, key properties of actual credit spreads are better captured by the model. Finally, the third essay proposes a model of interest rate swap spreads. The model accommodates both the default risk inherent in swap contracts and the liquidity difference between the swap and Treasury markets. The default risk and liquidity components of swap spreads are found to behave very differently: first, the default risk component is positively related to the riskless interest rate, whereas the liquidity component is negatively correlated with the riskless interest rate; second, although default risk accounts for the largest share of the levels of swap spreads, the liquidity component is much more volatile; and finally, while the default risk component has been historically positive, the liquidity component was negative for much of the 1990s and has become positive since the financial market turmoil in 1998.

This dissertation is in the form of three essays on the topic of component and long memory GARCH models. The unifying feature of the thesis is the focus on investigating European index option evaluation using these models. / The first essay presents a new model for the valuation of European options. In this model, the volatility of returns consists of two components. One of these components is a long-run component that can be modeled as fully persistent. The other component is short-run and has zero mean. The model can be viewed as an affine version of Engle and Lee (1999), allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature. It also fits options better than a model that combines conditional heteroskedasticity and Poisson normal jumps. While the improvement in the component model's performance is partly due to its improved ability to capture the structure of the smirk and the path of spot volatility, its most distinctive feature is its ability to model the term structure. This feature enables the component model to jointly model long-maturity and short-maturity options. / The second essay derives two new GARCH variance component models with non-normal innovations. One of these models has an affine structure and leads to a closed-form option valuation formula. The other model has a non-affine structure and hence, option valuation is carried out using Monte Carlo simulation. We provide an empirical comparison of these two new component models and the respective special cases with normal innovations. We also compare the four component models against GARCH(1,1) models which they nest. All eight models are estimated using MLE on S&P500 returns. The likelihood criterion strongly favors the component models as well as non-normal innovations. The properties of the non-affine models differ significantly from those of the affine models. Evaluating the performance of component variance specifications for option valuation using parameter estimates from returns data also provides strong support for component models. However, support for non-normal innovations and non-affine structure is less convincing for option valuation. / The third essay aims to investigate the impact of long memory in volatility on European option valuation. We mainly compare two groups of GARCH models that allow for long memory in volatility. They are the component Heston-Nandi GARCH model developed in the first essay, in which the volatility of returns consists of a long-run and a short-run component, and a fractionally integrated Heston-Nandi GARCH (FIHNGARCH) model based on Bollerslev and Mikkelsen (1999). We investigate the performance of the models using S&P500 index returns and cross-sections of European options data. The component GARCH model slightly outperforms the FIGARCH in fitting return data but significantly dominates the FIHNGARCH in capturing option prices. The findings are mainly due to the shorter memory of the FIHNGARCH model, which may be attributed to an artificially prolonged leverage effect that results from fractional integration and the limitations of the affine structure.

Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the empirical shortcomings of this model. In the first essay, we investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on a long sample of S& P500 returns. Finally, we employ nonlinear least squares on a time series of cross sections of option data. In the estimations on returns and options data, we use the particle filtering technique to retrieve the spot volatility path. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of alternative volatility specifications is a model we refer to as the VAR model, which is of the GARCH diffusion type. / In the second essay, we estimate the Constant Elasticity of Variance (CEV) model in order to study the level of nonlinearity in the volatility dynamic. We also estimate a CEV process combined with a jump process (CEVJ) and analyze the effects of the jump component on the nonlinearity coefficient. Estimation is performed using the particle filtering technique on a long series of S&P500 returns and on options data. We find that both returns data and returns-and-options data favor nonlinear specifications for the volatility dynamic, suggesting that the extensive use of linear models is not supported empirically. We also find that the inclusion of jumps does not affect the level of nonlinearity and does not improve the CEV model fit. / The third essay provides an empirical comparison of two classes of option valuation models: continuous-time models and discrete-time models. The literature provides some theoretical limit results for these types of dynamics, and researchers have used these limit results to argue that the performance of certain discrete-time and continuous-time models ought to be very similar. This interpretation is somewhat contentious, because a given discrete-time model can have several continuous-time limits, and a given continuous-time model can be the limit for more than one discrete-time model. Therefore, it is imperative to investigate whether there exist similarities between these specifications from an empirical perspective. Using data on S&P500 returns and call options, we find that the discrete-time models investigated in this paper have the same performance in fitting the data as selected continuous-time models both in and out-of-sample.

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A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 2017 / The period from 2006 to 2015 was a turbulent one for mining companies. The end of the 2000s commodity super cycle resulted in all-time high market values for most commodity based companies, followed by a rapid decline in value with the onset of the Global Financial Crisis in 2008 and a similar rapid recovery following this. Whilst much of this change in value was driven by commodity prices, the inconsistent performance between companies suggests that there are other factors affecting mining company value. To determine the key drivers of company value, four diversified and international mining companies which represent close to 50% of the 2006 industry revenue were selected for analysis. These were Anglo American, BHP Billiton, Rio Tinto and CVRD-Vale. Financial and production data was collected to analyse different potential value drivers. Because of its suitability for comparison of company value, the market based valuation approach was selected as the company valuation technique. Enterprise value (EV) was the metric used for company value since this provides a measure of the real market value of a firm as a whole business. Eight potential value drivers, which include production output, commodity price, revenue, EBITDA margin, EBITDA multiple, gearing ratio, net debt to EBITDA ratio and ROCE, were selected for analysis. Each potential value driver was tracked against EV to determine if there was any correlation between the value driver and EV. Also, the Pearson correlation method was used to determine correlation between each potential value driver and EV. Production output and commodity price in isolation were found not to drive company value. However, when combined to calculate revenue, had a very high correlation to EV with an average Pearson coefficient of 0.8. EBITDA multiple was also found to be a key driver of company value, with this metric closely aligned to revenue (Pearson coefficient of 0.6). The two debt metrics, gearing ratio and net debt to EBITDA were found to only have a correlation to EV in times of declining commodity prices and revenue. EBITDA margin and ROCE were found to have no correlation to EV and as such were not considered to be key drivers of company value. Mining companies must ensure that they focus on the correct value drivers to ensure those they influence do impact the company value. / MT 2017

Tang Hoi-man = 受抵押品保護的公司債券的估值 / 鄧凱文. / Thesis submitted in: December 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 69-72). / Text in English; abstracts in English and Chinese. / Tang Hoi-man = Shou di ya pin bao hu de gong si zhai quan de gu zhi / Deng Kaiwen. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.3 / Chapter 2.1 --- Review of Merton Model [24] --- p.4 / Chapter 2.1.1 --- Refinement of the Structural Model --- p.6 / Chapter 2.2 --- "Hui, Lo, Huang and Lee model" --- p.8 / Chapter 2.3 --- Recent models consider the PD-RR relationship --- p.11 / Chapter 2.3.1 --- Frye model --- p.11 / Chapter 2.3.2 --- Jokivuolle and Peura model --- p.12 / Chapter 3 --- The Valuation of Collateralized Corporate Bond --- p.13 / Chapter 3.1 --- The framework of the Model --- p.13 / Chapter 3.2 --- The Valuation of Collateralized Corporate Bond --- p.17 / Chapter 3.2.1 --- Derivation of Collateralized Corporate Bond --- p.18 / Chapter 3.2.2 --- "Relation between Proposed Model and Hui, Lo, Huang and Lee Model" --- p.22 / Chapter 4 --- The Study of the Closed-form Solution --- p.24 / Chapter 4.1 --- Applications --- p.24 / Chapter 4.1.1 --- Probabilities of Default --- p.25 / Chapter 4.1.2 --- Expected Loss-given-default --- p.26 / Chapter 4.2 --- Closed-form solution and Monte-Carlo Simulation --- p.29 / Chapter 4.2.1 --- Closed-form Solution --- p.29 / Chapter 4.2.2 --- Monte-Carlo Simulation --- p.31 / Chapter 4.2.3 --- Comparison between Closed-form Solution and Monte- carlo Simulation --- p.33 / Chapter 5 --- Data Analysis and Discussion --- p.38 / Chapter 5.1 --- Effects on ELGD of Different Parameters --- p.38 / Chapter 5.1.1 --- "Effect of Initial Collateral Value, S0" --- p.39 / Chapter 5.1.2 --- "Effect of Collateral's Volatility, σs" --- p.39 / Chapter 5.1.3 --- "Effect of Correlation between Firm's Leverage Ratio and Collateral, pLS" --- p.40 / Chapter 5.1.4 --- "Effect of residue recovery rate, δ" --- p.40 / Chapter 5.1.5 --- "Effect of Maturity, T" --- p.41 / Chapter 5.2 --- Initial Setting of Parameters --- p.42 / Chapter 5.3 --- Effects on ELGD for Different Rated Firms --- p.43 / Chapter 5.3.1 --- Effects on ELGD of Different S0 and σs --- p.45 / Chapter 5.3.2 --- Effect on ELGD of Different S0 and pLS --- p.47 / Chapter 5.3.3 --- Effect on ELGD of Different S0 and δ --- p.49 / Chapter 5.3.4 --- Effect on ELGD of Different S0 and T --- p.51 / Chapter 5.3.5 --- Effect on ELGD of Different and pLS --- p.53 / Chapter 5.3.6 --- Effect on ELGD of Different σs and δ --- p.55 / Chapter 5.3.7 --- Effect on ELGD of Different and T --- p.57 / Chapter 5.3.8 --- Effect on ELGD of Different pLS and δ --- p.59 / Chapter 5.3.9 --- Effect on ELGD of Different pLS and T --- p.61 / Chapter 5.3.10 --- Effect of on ELGD Different 6 and T --- p.63 / Chapter 5.4 --- Summary --- p.65 / Chapter 6 --- Conclusion --- p.67 / Bibliography --- p.69 / Chapter A --- Derivation of Pricing Equation --- p.73

Wong, Tat Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 53-55). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Problem Formulation --- p.5 / Chapter 2.1 --- Phase-type distribution --- p.5 / Chapter 2.1.1 --- A generalization of the exponential distribution --- p.5 / Chapter 2.1.2 --- Properties of the phase-type distribution --- p.6 / Chapter 2.2 --- Phase-type jump diffusion model --- p.8 / Chapter 2.2.1 --- Jump diffusion model --- p.8 / Chapter 2.2.2 --- The stock price model --- p.9 / Chapter 2.3 --- Stock Loans --- p.10 / Chapter 3 --- General Properties of Stock Loans --- p.12 / Chapter 3.1 --- Preliminary results --- p.12 / Chapter 3.2 --- Characterization of the function V(x) --- p.15 / Chapter 4 --- Valuation / Chapter 4.1 --- Hyperexponential jumps --- p.25 / Chapter 4.1.1 --- Solution of the linear system --- p.29 / Chapter 4.1.2 --- Solution of the optimal exercise boundary --- p.30 / Chapter 4.2 --- Phase-type jumps --- p.33 / Chapter 4.3 --- The case for G'(1)≥ 0 --- p.36 / Chapter 5 --- Future Research Direction --- p.38 / Chapter 5.1 --- The fast mean-reverting stochastic volatility model --- p.38 / Chapter 5.2 --- Asymptotic expansion of stock loan --- p.39 / Chapter 5.2.1 --- The zeroth order term --- p.41 / Chapter 5.2.2 --- The first order term --- p.43 / Chapter 6 --- Conclusion --- p.52 / Bibliography --- p.53