A Duality Result for Robust Optimization with Expectation Constraints

TL;DR

This paper introduces a convex optimization approach to solve expectation-constrained robust maximization problems, with applications to financial derivatives pricing and super-replication, simplifying previous complex methods.

Contribution

It encodes super-replication problems into a single convex minimization framework, enabling practical computation of no-arbitrage bounds for various financial derivatives.

Findings

Developed a convex minimization formulation for super-replication

Applied the method to bounds on forward-starting options and swaps

Produced easily-implementable sparse linear programs

Abstract

This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial derivatives. While the previous literature has connected super-replication values to a convex minimization problem whose objective function is related to a sequence of iterated concave envelopes, we show how this whole process can be encoded in a single convex minimization problem. The natural finite-dimensional approximation of this minimization problem results in an easily-implementable sparse linear program. We highlight this technique by obtaining no-arbitrage bounds on the prices of forward-starting options, continuously-monitored variance swaps, and discretely-monitored gamma swaps, each subject to observed bid-ask spreads of finitely-many vanilla options.