Optimal exercise decision of American options under model uncertainty

Paper: arXiv 2310.14473

Authors: Tongseok Lim

Abstract

Given the marginal distribution information of the underlying asset price at two future times $T_1$ and $T_2$, we consider the problem of determining a model-free upper bound on the price of a class of American options that must be exercised at either $T_1$ or $T_2$. The model uncertainty consistent with the given marginal information is described as the martingale optimal transport problem. We show that any option exercise scheme associated with any market model that jointly maximizes the expected option payoff must be nonrandomized if the American option payoff satisfies a suitable convexity condition and the model-free price upper bound and its relaxed version coincide. The latter condition is desired to be removed under appropriate conditions on the cost and marginals.

Complexity vs Empirical Score

• Math Complexity: 0.0/10
• Empirical Rigor: 0.0/10
• Quadrant: Philosophers — conceptual discussion, limited math and data

Why this score: Scoring failed: Could not find valid JSON in LLM response: line 1 column 1 (char 0)

Research Flowchart

  flowchart TD
    A["Research Goal: Find model-free upper bound for 2-period (T1, T2) American option prices under model uncertainty"] --> B["Inputs: Marginal distributions at T1 & T2, Option Payoff with convexity condition"]
    B --> C["Formulate Martingale Optimal Transport (MOT) Problem & Relaxed Version"]
    C --> D["Analyze Optimality & Relaxation Equivalence Conditions"]
    D --> E["Key Finding: Optimal exercise scheme is nonrandomized when price upper bound matches its relaxed version"]