When are Swing options bang-bang and how to use it

TL;DR

This paper analyzes swing options with firm constraints, showing their premium is concave and piecewise affine, and introduces a quantization-based recursive method for pricing, with error bounds.

Contribution

It establishes conditions for bang-bang controls and develops a recursive pricing method with error bounds for swing options.

Findings

Premium function is concave and piecewise affine.

Bang-bang optimal controls exist under certain constraints.

A quantization-based recursive pricing algorithm with error bounds.

Abstract

In this paper we investigate a class of swing options with firm constraints in view of the modeling of supply agreements. We show, for a fully general payoff process, that the premium, solution to a stochastic control problem, is concave and piecewise affine as a function of the global constraints of the contract. The existence of bang-bang optimal controls is established for a set of constraints which generates by affinity the whole premium function. When the payoff process is driven by an underlying Markov process, we propose a quantization based recursive backward procedure to price these contracts. A priori error bounds are established, uniformly with respect to the global constraints.