Fair bilateral prices in Bergman's model

TL;DR

This paper extends Bergman's model to a nonlinear market setting, analyzing fair bilateral prices and hedging strategies for contracts considering initial endowments, using BSDEs and PDEs.

Contribution

It introduces inequalities for unilateral prices and characterizes the range of fair bilateral prices in a nonlinear market model with multiple assets and accounts.

Findings

Derived inequalities for unilateral prices

Established the range for fair bilateral prices

Analyzed monotonicity of prices with respect to initial endowment

Abstract

Bielecki and Rutkowski (2014) introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts and margin accounts. In this paper, we examine the pricing and hedging of contract both from the perspective of the hedger and the counterparty with arbitrary initial endowments. We derive inequalities for unilateral prices and we give the range for either fair bilateral prices or bilaterally profitable prices. We also study the monotonicity of a unilateral price with respect to the initial endowment. Our study hinges on results for BSDE driven by continuous martingales obtained in Nie and Rutkowski (2014), but we also derive the pricing PDEs for path-independent contingent claims of European style in a Markovian framework.