Monte Carlo valuation of energy options: From spread to swing.

摘要

Monte Carlo simulation has been a widely used approach for option pricing. Under the concept of risk neutrality, the value of an option is equivalent to its expected payoff, which can be written as an integral. When an integral is multi-dimensional, like most of the cases in option pricing, evaluating the integral analytically becomes impractical. Nevertheless, Monte Carlo simulation provides a simple and straightforward way of approximating the integral. It is especially powerful in cases where no closed form pricing formulas can be derived. In this paper, we intend to use Monte Carlo simulation as the main tool for the pricing of spread options and swing options for which there are no closed form formulas available.;We begin with evaluating the price of a spread option whose payoff depends on the difference between the price of one fuel and the minimum of the prices of other N fuels plus the strike price. An efficient numerical method that combines the ideas from simulation and variance reduction techniques such as conditioning and stratified sampling is proposed. Our method uses deterministic sample instead of random sample as input. Comparing to the crude Monte Carlo simulation, we show that we are able to approximate the option price accurately by using only a small set of fixed values as input for the evaluation.;For the pricing of options with multiple early exercise opportunities that are known as swing options in the energy market, approaches suggested in the literature with accurate numerical results are computationally demanding. With that in mind, we introduce a more efficient way to apply Monte Carlo simulation to the valuation of a simplified version of swing option. Our approach calculates lower and upper bounds of the option price by using different exercise strategies that capture the features of the optimal exercise strategy. The result shows that with adequate choice of exercise strategies, our method provides a satisfying approximation of the option price with much less computing effort than other approaches.