Efficient optimization algorithms for pricing energy derivatives and standard vanilla options

Our first study researched a problem of scheduling operational flexibility of electricity generating facilities. Recently, a number of new approaches based on stochastic dynamic programming techniques have been suggested in the academic literature. Although these approaches are flexible in terms of incorporating various operational constraints, they are computationally inefficient when considering problems with relatively large horizons. Here we suggest a simple framework that is computationally efficient as well as numerically robust when dealing with large horizon problems. We show that the optimal dispatch policy can be characterized through a set of optimal exercise boundaries and also theoretically derive the shape properties of the boundaries. The problem of finding the optimal exercise boundaries is then reduced to solving a simple linear programming problem. The suggested approach is flexible in incorporating various real world operational constraints. We compare the computational performance of the suggested scheme with alternative dynamic programming based methods. Our second study considered a regression approach to pricing European options in an incomplete market. The algorithm replicates an option by a portfolio consisting of the underlying security and a risk-free bond. We apply linear regression framework and quadratic programming with linear constraints (input = sample paths of underlying security; output = table of option prices as a function of time and price of the underlying security). We populate the model with historical prices of the underlying security (possibly 10 massaged to the present volatility) or with Monte Carlo simulated prices. Risk neutral processes or probabilities are not needed in this framework