The various models have been built upon pioneering work of Robert F. Engle (2003) and Robert C. Merton (1997) for methods of analyzing economic time series with time-varying volatility and a new method to determine the value of derivatives, respectively. This book fills the gaps which Harry M. Markowitz’s (1990) mean-variance analysis fails to capture. Especially, this book investigates dynamic processes of asset returns, volatility, and jumps which are time-varying and stochastic in discrete- and continuous-time settings. I demonstrate that these additional computational and modeling efforts provide us with significant benefits to better capture actual financial time-series data and to reduce option pricing errors. If we only consider mean and variance as in Markowitz, most likely we may not fully appreciate recent advances in risk managements, investments, and derivatives pricing since many researchers recognize the importance of economic and statistical roles of skewness and kurtosis. To better explain well-known skewness and excess kurtosis of financial time-series returns, I employ asymmetric fat-tailed distributions such as Hansen's skewed t-distribution and Lévy jump models.