This thesis addresses the modeling of energy prices with time-varying volatility and jumps in three separate and self-contained papers: A. Modeling energy futures volatility through stochastic volatility processes with Markov chain Monte Carlo This paper studies the volatility dynamics of futures contracts on crude oil, natural gas and electricity. To accomplish this purpose, an appropriate Bayesian model comparison exercise between seven stochastic volatility (SV) models and their counterpart GARCH models is performed, with both classes of time-varying volatility processes being estimated through a Markov chain Monte Carlo technique. A comparison exercise for hedging purposes is also considered by computing the extreme risk measures (using the Conditional Value-at-Risk) of simulated returns from the SV model with the best performance - i.e., the SV model with a t-distribution - and the standard GARCH(1,1) model for the hedging of crude oil, natural gas and electricity positions. Overall, we find that: (i) volatility plays an important role in energy futures markets; (ii) SV models generally outperform their GARCH-family counterparts; (iii) a model with t-distributed innovations generally improves the fitting performance of both classes of time-varying volatility models; (iv) the maturity of futures contracts matters; and (v) the correct specification for the stochastic behavior of futures prices impacts the extreme market risk measures of hedged and unhedged positions. B. How does electrification under energy transition impact the portfolio management of energy firms? This paper presents a novel approach for structuring dependence between electricity and natural gas prices in the context of energy transition: a copula of meanreverting and jump-diffusion processes. Based on historical day-ahead prices of the Nord Pool electricity market and the Henry Hub natural gas market, a stochastic model is estimated via the maximum likelihood approach and considering the dependency structure between the innovations of these two-dimensional returns. Given the role of natural gas in the global policy for energy transition, different copula functions are fit to electricity and natural gas returns. Overall, we find that: (i) using an out-of-sample forecasting exercise, we show that it is important to consider both mean-reversion and jumps; (ii) modeling correlation between the returns of electricity and natural gas prices, assuring nonlinear dependencies are satisfied, leads us to the adoption of Gumbel and Student-t copulas; and (iii) without government incentive schemes in renewable electricity projects, the usual maximization of the risk-return trade-off tends to avoid a high exposure to electricity assets. C. Modeling commodity prices under alternative jump processes and fat tails dynamics The recent fluctuations in commodity prices affected significantly Oil Gas (O&G) companies’ returns. However, integrated O&G companies are not only exposed to the downturn of oil prices since a high level of integration allows these firms to obtain non-perfectly positive correlated portfolio. This paper aims to test several different stochastic processes to model the main strategic commodities in integrated O&G companies: brent, natural gas, jet fuel and diesel. The competing univariate models include the log-normal and double exponential jump-diffusion model, the Variance-Gamma process and the geometric Brownian motion with nonlinear GARCH volatility. Given the effect of correlation between these assets, we also estimate multivariate models, such as the Dynamic Conditional Correlation (DCC) GARCH, DCC-GJR-GARCH and the DCC-EGARCH models. Overall, we find that: (i) the asymmetric conditional heteroskedasticity model substantially improves the performance of the univariate jump-diffusion models; and (ii) the multivariate approaches are the best models for our strategic energy commodities, in particular the DCC-GJR-GARCH model.