Swing Option Pricing by Optimal Exercise Boundary Estimation

Abstract

This paper introduces an original and competitive Monte Carlo algorithm for the valuation of multiple exercises options known as swing options on energy markets, with the two hypotheses that there is only one source of uncertainty and that the market is complete. A swing option is a contract which gives the right (not the obligation) to the purchaser to buy (call) or sell (put) a fixed quantity of energy, at a fixed price, for a fixed number of times chosen in a set of possible dates. These securities are an extension of Bermudean options and are widely used in the energy sector to optimize energy stocks contracts. With one source of uncertainty, deterministic approaches are more efficient to treat the problem if the uncertainty process is explicitly known. However, in pratcice, the process is often not explicitly known, and a Monte Carlo method could be usefull to solve the problem.

The algorithm is based on the search of the optimal exercise boundary. At a given date of exercise, the number of remaining exercise rights being known, this optimal exercise boundary is defined by an optimal market price above which (call) or under which (put) the option should be optimally exercised. Contrary to standard Monte Carlo methods, no supplementary parameter such as basis functions are needed to solve the problem.

This paper is divided in three distincts parts. First, proofs of the method are given under a certain number of conditions on the price process. Then, an implementation of the algorithm is presented, the algorithm only requiring a sort function. Finally, some comparison results with the classical Longstaff-Schwartz Monte Carlo algorithm are presented. The method appears less computationally demanding than the Longstaff-Schwartz method. Moreover, the optimal exercise boundary is derived explicitly. Given the quality of the method in dimension one, an extension in the multidimensional case seems to be an interesting challenge.

MSC codes: 49L20