Tug-of-war, market manipulation and option pricing

TL;DR

This paper introduces a novel option pricing model based on a tug-of-war game, capturing market manipulation dynamics through a two-player stochastic differential game in a multi-dimensional financial setting.

Contribution

It formulates a new two-player zero-sum game model for option pricing and proves the existence and uniqueness of the value function as a viscosity solution to a complex PDE.

Findings

The game has a well-defined value.

The value function solves a nonlinear PDE involving the infinity Laplace operator.

The model captures market manipulation strategies.

Abstract

We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the non-linear and completely degenerate infinity Laplace operator.