This dissertation consists of three essays. Chapter 1 is titled “Calibration for multivariate bilateral gamma model”. In this chapter, we discuss the multivariate bilateral gamma (MBG) model, which is an extension of the multivariate variance gamma (MVG) model that consists of predetermined Bilateral Gamma (BG) marginals. This model is used to model financial asset returns that have excess kurtosis, negative skewness, and asymmetry in the upward and downward motions. An efficient Monte Carlo simulation schema of this process is devised. Moreover, we propose an estimation procedure for the MBG modelbased on the Continuum Generalized Method of Moments (CGMM) and reparameterization of its correlation matrix. We compare this model with the full Gaussian copula (FGC) model by fitting it to the US equity data in the Dow Jones index, and the result indicates that the MBG model outperforms significantly. Chapter 2 is titled “Pairs trading strategies: Distance, cointegration, copula, and MBG method”. In this chapter, we propose a new method of building pairs trading strategy that uses MBG to model the dependency structure of stock pairs. The trading signal is then built based on the cumulative mispricing indexes, which are calculated using the conditional probability of the MBG distribution. We also conduct a comprehensive study on the performance of four different pairs trading strategies—the distance, cointegration, copula, and MBG methods—on the US equity market from 2016 to 2019. The result shows that the MBG method has the highest excess return and records the best risk-adjusted performance. Chapter 3 is titled “Predictability of corporate bond returns with machine learning.” This chapter performs a comparative analysis of machine learning methods for the predictability of corporate bonds returns. We found that machine learning models, especially ensemble learning methods like boosting, substantially improve the out-of-sample performance of stock and bond characteristics in predicting future bond returns. We also show that portfolios constructed using the prediction of machine learning models contribute to economic gains. To investigate which features the models rely on when making a prediction, we discuss three methods for calculating feature importance, including SHapley Additive exPlanations(SHAP) based on Shapley value. This method is model agnostic, consistent, and can provide an explanation for each observation. We also discuss the performance of the parsimonious model with the 15 most important features selected by SHAP.