This thesis models rational criminals and regulators with flawed incentives. In it we develop a rational model of crime and regulation that we use to show the SEC's current incentive structure is ineffective at preventing fraud. Under our model, criminals balance the monetary rewards of larger frauds against an increased chance of being apprehended; and regulators design regulations to minimize either the damage caused by fraud or some other metric. We show that under this model, the SEC's focus on 'stats' and 'quick hits' leads to large frauds and a large social loss. We argue that regulators need to focus not just on successful prosecutions, but also on harm reduction and deterrence.

Stochastic control is a broad tool with applications in several areas of academic interest. The financial literature is full of examples of decisions made under uncertainty and stochastic control is a natural framework to deal with these problems. Problems such as optimal trading, option pricing and economic policy all fall under the purview of stochastic control. These problems often face nonlinearities that make analytical solutions infeasible and thus numerical methods must be employed to find approximate solutions. In this dissertation three types of stochastic control formulations are used to model applications in finance and numerical methods are developed to solve the resulting nonlinear problems. To begin with, optimal stopping is applied to option pricing. Next, impulse control is used to study the problem of interest rate control faced by a nation's central bank, and finally a new type of hybrid control is developed and applied to an investment decision faced by money managers. / text

This thesis models rational criminals and regulators with flawed incentives. In it we develop a rational model of crime and regulation that we use to show the SEC's current incentive structure is ineffective at preventing fraud. Under our model, criminals balance the monetary rewards of larger frauds against an increased chance of being apprehended; and regulators design regulations to minimize either the damage caused by fraud or some other metric. We show that under this model, the SEC's focus on 'stats' and 'quick hits' leads to large frauds and a large social loss. We argue that regulators need to focus not just on successful prosecutions, but also on harm reduction and deterrence.

In this thesis, we provide several applications of Gram-Charlier expansions in derivative pricing. We first give an exposition on how to calculate swaption prices under the the CIR2 model. Then we extend this method to CIR2++ model. We also develop a procedure to calculate European call options under Heston’s model of stochastic volatility by Gram-Charlier Expansions.

We analyze the nature of sovereign credit risk for selected Asian and European countries through a set of sovereign CDS data for an eighty-year period that includes the episode of the 2008-2009 financial crisis. Our principal component analysis results suggest that there is strong commonality in sovereign credit risk across countries after the crisis. The regression tests show that the commonality is linked to both local and global financial and economic variables. Besides, we also notice intriguing differences in the sovereign credit risk behavior of Asian and European countries. Specifically, we find that some variables, including foreign reserve, global stock market, and volatility risk premium, affect the of Asian and European sovereign credit risks in the opposite direction. Further, we assume that the arrival rates of credit events follow a square-root diffusion from which we build our pricing model. The resulting model is used to decompose credit spreads into risk premium and credit-event components.

In this thesis, we provide several applications of Gram-Charlier expansions in derivative pricing. We first give an exposition on how to calculate swaption prices under the the CIR2 model. Then we extend this method to CIR2++ model. We also develop a procedure to calculate European call options under Heston’s model of stochastic volatility by Gram-Charlier Expansions.

We analyze the nature of sovereign credit risk for selected Asian and European countries through a set of sovereign CDS data for an eighty-year period that includes the episode of the 2008-2009 financial crisis. Our principal component analysis results suggest that there is strong commonality in sovereign credit risk across countries after the crisis. The regression tests show that the commonality is linked to both local and global financial and economic variables. Besides, we also notice intriguing differences in the sovereign credit risk behavior of Asian and European countries. Specifically, we find that some variables, including foreign reserve, global stock market, and volatility risk premium, affect the of Asian and European sovereign credit risks in the opposite direction. Further, we assume that the arrival rates of credit events follow a square-root diffusion from which we build our pricing model. The resulting model is used to decompose credit spreads into risk premium and credit-event components.

With the development of various derivative instruments and index products, commodities have become a distinct asset class which can offer enhanced diversification benefits to the traditional asset allocation of stocks and bonds. In this thesis, we begin by discussing some of the key properties of commodity markets which distinguish them from bond and stock markets. Then, we consider the informational role of commodity futures markets. Since commodity prices exhibit mean-reverting behaviour, we will also review several mean-reversion models which are commonly used to capture and describe the dynamics of commodity prices. In Chapter 4, we focus on discussing a two-factor mean-reverting model proposed by Hikspoors and Jaimungal, as a means of providing additional degree of randomness to the long-run mean level. They have also suggested a method to extract the implied market prices of risk, after estimating both the risk-neutral and real-world parameters from the calibration procedure. Given the usefulness of this model, we are motivated to investigate the robustness of this calibration process by applying the methodology to simulated data. The capability to produce stable and accurate parameter estimates will be assessed by selecting various initial guesses for the optimization process. Our results show that the calibration method had a lot of difficulties in estimating the volatility and correlation parameters of the model. Moreover, we demonstrate that multiple solutions obtained from the calibration process would lead to model uncertainty in extracting the implied market prices of risk. Finally, by using historical crude oil data from the same time period, we can compare our calibration results with those obtained by Hikspoors and Jaimungal.

With the development of various derivative instruments and index products, commodities have become a distinct asset class which can offer enhanced diversification benefits to the traditional asset allocation of stocks and bonds. In this thesis, we begin by discussing some of the key properties of commodity markets which distinguish them from bond and stock markets. Then, we consider the informational role of commodity futures markets. Since commodity prices exhibit mean-reverting behaviour, we will also review several mean-reversion models which are commonly used to capture and describe the dynamics of commodity prices. In Chapter 4, we focus on discussing a two-factor mean-reverting model proposed by Hikspoors and Jaimungal, as a means of providing additional degree of randomness to the long-run mean level. They have also suggested a method to extract the implied market prices of risk, after estimating both the risk-neutral and real-world parameters from the calibration procedure. Given the usefulness of this model, we are motivated to investigate the robustness of this calibration process by applying the methodology to simulated data. The capability to produce stable and accurate parameter estimates will be assessed by selecting various initial guesses for the optimization process. Our results show that the calibration method had a lot of difficulties in estimating the volatility and correlation parameters of the model. Moreover, we demonstrate that multiple solutions obtained from the calibration process would lead to model uncertainty in extracting the implied market prices of risk. Finally, by using historical crude oil data from the same time period, we can compare our calibration results with those obtained by Hikspoors and Jaimungal.

Aggregating financial assets together to form a portfolio, commonly referred to as "asset pooling", is a standard practice in the banking and insurance industries. Determining a suitable probability distribution for this portfolio with each underlying asset is a challenging task unless several distributional assumptions are made. On the other hand, imposing assumptions on the distribution inhibits its ability to capture various idiosyncratic behaviors. It limits the model's usefulness in its ability to provide realistic risk metrics of the true portfolio distribution. In order to conquer this limitation, we propose two methods to model a pool of assets with much less assumptions on the correlation structure by way of finding analytical bounds. Our first method uses the Fre??chet-Hoeffding copula bounds to calculate model-free upper and lower bounds for aggregate assets evaluation. For the copulas with specific constraints, we improve the Fre??chet- Hoeffding copula bounds by providing bounds with narrower range. The improvements proposed are very robust for different types of constraints on the copula function. However, the lower copula bound does not exist for dimension three and above. Our second method tackles the open problem of finding lower bounds for higher dimensions by introducing the concept of Complete Mixability property. With such technique, we are able to find the lower bounds with specified constraints. Three theorems are proposed. The first theorem deals with the case where all marginal distributions are identical. The lower bound defined by the first theorem is sharp under some technical assumptions. The second theorem gives the lower bound in a more general setup without any restriction on the marginal distributions. However the bound achieved in this context is not sharp. The third theorem gives the sharp lower bound on Conditional VaR. Numerical results are provided for each method to demonstrate sharpness of the bounds. Finally, we point out some possible future research directions, such as looking for a general sharp lower bound for high dimensional correlation structures.