A First-Order BSPDE for Swing Option Pricing

TL;DR

This paper introduces a novel first-order non-linear backward stochastic partial differential equation to model swing option pricing in a non-Markovian continuous-time setting, providing new insights into optimal control and duality.

Contribution

It establishes that the swing option value process solves a first-order BSPDE and characterizes optimal controls and dual problems in a general non-Markovian context.

Findings

Value process solves a first-order non-linear BSPDE

Characterization of optimal controls

Derivation of a dual minimization problem

Abstract

We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal controls and derive a dual minimization problem.