A Splitting Equilibration Algorithm for the Computation of Large-Scale Constrained Matrix Problems; Theoretical Analysis and Applications

In this paper we introduce a general parallelizable computational method for solving a wide spectrum of constrained matrix problems. The constrained matrix problem is a core problem in numerous applications in economics. These include the estimation of input/output tables, trade tables, and social/national accounts, and the projection of migration flows over space and time. The constrained matrix problem, so named by Bacharach, is to compute the best possible estimate X of an unknown matrix, given some information to constrain the solution set, and requiring either that the matrix X be a minimum distance from a given matrix, or that X be a functional form of another matrix. In real-world applications, the matrix X is often very large (several hundred to several thousand rows and columns), with the resulting constrained matrix problem larger still (with the number of variables on the order of the square of the number of rows/columns; typically, in the hundreds of thousands to millions). In the classical setting, the row and column totals are known and fixed, and the individual entries nonnegative. However, in certain applications, the row and column totals need not be known a priori, but must be estimated, as well. Furthermore, additional objective and subjective inputs are often incorporated within the model to better represent the application at hand. It is the solution of this broad class of large-scale constrained matrix problems in a timely fashion that we address in this paper. The constrained matrix problem has become a standard modelling tool among researchers and practitioners in economics. Therefore, the need for a unifying, robust, and efficient computational procedure for solving constrained matrix problems is of importance. Here we introduce a.n algorithm, the splitting equilibration algorithm, for computing the entire class of constrained matrix problems. This algorithm is not only theoretically justiflid, hilt l'n fi,1 vl Pnitsf htnh thP lilnlprxing s-trlrtilre of thpCp !arop-Cspe mrnhlem nn the advantages offered by state-of-the-art computer architectures, while simultaneously enhancing the modelling flexibility. In particular, we utilize some recent results from variational inequality theory, to construct a splitting equilibration algorithm which splits the spectrum of constrained matrix problems into series of row/column equilibrium subproblems. Each such constructed subproblem, due to its special structure, can, in turn, be solved simultaneously via exact equilibration in closed form. Thus each subproblem can be allocated to a distinct processor. \We also present numerical results when the splitting equilibration algorithm is implemented in a serial, and then in a parallel environment. The algorithm is tested against another much-cited algorithm and applied to input/output tables, social accounting matrices, and migration tables. The computational results illustrate the efficacy of this approach

Optimal quantization for the pricing of swing options

In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz algorithm.Comment: 27

A model for hedging load and price risk in the Texas electricity market

Energy companies with commitments to meet customers’ daily electricity demands face the problem of hedging load and price risk. We propose a joint model for load and price dynamics, which is motivated by the goal of facilitating optimal hedging decisions, while also intuitively capturing the key features of the electricity market. Driven by three stochastic factors including the load process, our power price model allows for the calculation of closed-form pricing formulas for forwards and some options, products often used for hedging purposes. Making use of these results, we illustrate in a simple example the hedging benefit of these instruments, while also evaluating the performance of the model when fitted to the Texas electricity market

The valuation of clean spread options: linking electricity, emissions and fuels

The purpose of the paper is to present a new pricing method for clean spread options, and to illustrate its main features on a set of numerical examples produced by a dedicated computer code. The novelty of the approach is embedded in the use of a structural model as opposed to reduced-form models which fail to capture properly the fundamental dependencies between the economic factors entering the production process

Efficient pricing of discrete arithmetic Asian options under mean reversion and jumps based on Fourier-cosine expansions

We propose an efficient pricing method for arithmetic Asian options based on Fourier-cosine expansions. In particular, we allow for mean reversion and jumps in the underlying price dynamics. There is an extensive body of empirical evidence in the current literature that points to the existence and prominence of such anomalies in the prices of certain asset classes, such as commodities. Our efficient pricing method is derived for the discretely monitored versions of the European-style arithmetic Asian options. The analytical solutions obtained from our Fourier-cosine expansions are compared to the benchmark fast Fourier transform based pricing for the examination of its accuracy and computational efficienc

A non-parametric structural hybrid modeling approach for electricity prices

We develop a stochastic model of zonal/regional electricity prices, designed to reflect information in fuel forward curves and aggregated capacity and load as well as zonal or regional price spreads. We use a nonparametric model of the supply stack that captures heat rates and fuel prices for all generators in the market operator territory, combined with an adjustment term to approximate congestion and other zone-specific behavior. The approach requires minimal calibration effort, is readily adaptable to changing market conditions and regulations, and retains sufficient tractability for the purpose of forward price calibration. The model is illustrated for the spot and forward electricity prices of the PS zone in the PJM market, and the set of time-dependent risk premiums are inferred and analyzed

Valuation Of Continuously Monitored Double Barrier Options And Related Securities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/92059/1/j.1467-9965.2010.00469.x.pd