An Overview Of Energy Commodity And Basic Derivatives In Modeling And Pricing

Energy resources are the decisive resources in the development of the world economy. So energy security problems are highly thought of by a large number of goverments and academics. During the rapid development of energy market, we need to manage and control all kinds of risk, in which the control of energy price risk is the most important. In order to guarantee the stability of energy prices, energy-related enterprises must take measures in advance and prevent the business risks caused by the large price fluctuations. It is required that we should carry out risk management, in which the energy derivatives is considered an important factor. Hence, it is very important to develop the energy derivatives for the improvement of Chinese energy market. At present, in the energy market, the main source of energy derivatives includes forward contracts, futures, options and swaps. Even though the energy derivatives and financial derivatives products have a lot in common, but they also have a lot of differences, such as electricity can not be stored, the characteristicsof instantaneous transactions, energy commodities, such as complementary characteristics, making the pricing of energy derivatives more complicated than the pricing of financial derivatives.First, this paper sums up the price models of energy commodities for the basic characteristics of energy commodities. The first model which can describes the energy prices is the Geometric Brownian motionwhereμis the expected return rate,σis the volatility, dW_t is the standard Brown motion. But Geometric Brownian motion can not reflect the mean-reversion of energy prices. In fact, in the long term, energy prices have a mean-reversion, that iswhere k is the mean-reverting coefficients;θis the long term means. This article had a data simulation to the price of crude oil in the United States from 1861 to 2006 using SAS software. It verified the crude oil prices do have a mean-reversion. Besides, with mean-reversion jump-diffusion model describes the phenomenon of spike energy prices, as well as taking into account the economic cycle or the impact of weather factors on the price of the regime-switching model. This paper particularly introducs two complementary models of energy commodity prices, such as mean-reverting jump-diffusion process with deterministic volatility, mean-reverting jump-diffusion process with stochastic volatility and different levels of mean-reversion to add a model of regime-switching model.Secondly, this article summarizes the transform function method in the energy derivatives pricing applications. Here, the main consideration of the energy derivatives are futures and options, in which options include the standard European call options and spreads option. The target energy price models are the mean-reverting jump-diffusion process with deterministic volatility, mean-reverting jump-diffusion process with stochastic volatility and regime-switching model. Known by the option pricing theory, the pricing of energy derivatives for the three price models mentioned above on math need to be resolved at the Numerical calculation of multi-dimensional problem, and the transform functions can be transformed into multi-dimensional problem to study low-dimensional problem, which will provide a numerical calculationfor convenience. Under the risk-neutral measure, give the general form of the transform functionwhere Q is the risk-neutral measure, u in Cⁿ, (?)_t in Rⁿ, (?)_t is a state vector process,(?) is a flow domain. Price model was obtained by the three corresponding transformfunctions, which after the pricing of European energy derivatives provides the premise and foundation.Finally, the use of transform function method and the key results from Duffie, Pan & Singleton[23] gives a pricing based on the average of two jump-diffusion model and the regime-switching model of futures, European call options and European spread call price call option. The futures price of commodity S_t at time t with delivery time T is The price of a European call option on commodity S with strike price K is given byThe time-t value of a European cross-commodity spread call option on two commodities is given bywhere i is the imaginary unit,φis the transform functions, (?)_t = (X₁, X₂,…, X_n), n is the types of energy commodities. The value of the three kinds of energy derivatives can be obtained as long as you put the transform functions into the above formula. As for the process of transform functions, need to address the issue of terminal value problem for the Riccati equation. Riccati equation and only in limited circumstances has the closed-form solution. Therefore the transform function and the price of the corresponding derivatives don't have the closed-form solution, which can only be achieved through numerical calculation. Thus, in this article the use of the model parameter values form Deng [6], we give three futures prices under the price models by Matlab.Through the summary of the price models of the energy commodity and the method of pricing derivatives, we note that even though the complex models of the energy commodity can simultaneously describe the mean-reversion, spike phenomenonand seasonal characteristics of the energy commodity price, because of this complexity it makes the parameters in the calculation excessive, and that the complexity of pricing derivatives also brought certain difficulties to the derivatives. In this paper, the transform function to some extent reduces the complexity in derivatives pricing. At present, this approach is applied well in the European contingent claim, but the advantage hasn't been seen in the American contingent claim.From the current study of energy derivatives, we need to make improvement in the price models of energy commodity, parameter estimation, the pricing methods of energy derivatives and numerical calculation, this work will provide a solid theoretical basis for energy risk management.