Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market

Paper: arXiv 2301.02912

Authors: Jarek Kędra, Assaf Libman, Victoria Steblovskaya

Abstract

We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide explicit formulas for the minimum cost super-hedging strategies for a wide class of European type multi-asset contingent claims. This class includes European basket call and put options, among others. Since a super-hedge is a non-self-financing arbitrage strategy, it produces non-negative local residuals, for which we also give explicit formulas. This paper completes the foundation started in previous work of the authors for the extension of our results to a more realistic market model.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents robust theoretical proofs and explicit mathematical formulas for minimum cost super-hedging in incomplete multi-asset binomial markets without assuming joint distributions. However, it is purely theoretical with no empirical backtesting or real market data validation, limiting its immediate practical application.

Research Flowchart

  flowchart TD
    A[Goal: Minimum Cost Super-Hedging in Multi-Asset Incomplete Binomial Market] --> B[Input: m ≥ 2 Risky Assets Binomial Model & European Contingent Claims]
    B --> C[Method: Analyze Joint Distribution Dynamics without Independence Assumptions]
    C --> D[Process: Calculate Non-Self-Financing Arbitrage & Local Residuals]
    D --> E[Outcome: Explicit Formulas for Super-Hedging Strategies]
    D --> F[Outcome: Explicit Formulas for Local Residuals]
    E --> G[Application: Optimal Super-Hedging for European Basket Call/Put Options]
    F --> G