Paper: arXiv 2307.09710
Authors: Julian Sester
Abstract
We study the influence of additional intermediate marginal distributions on the value of the martingale optimal transport problem. From a financial point of view, this corresponds to taking into account call option prices not only, as usual, for those call options where the respective future maturities coincide with the maturities of some exotic derivative but also additional maturities and then to study the effect on model-independent price bounds for the exotic derivative. We characterize market settings, i.e., combinations of the payoff of exotic derivatives, call option prices and marginal distributions that guarantee improved price bounds as well as those market settings that exclude any improvement. Eventually, we showcase in numerous examples that the consideration of additional price information on vanilla options may have a considerable impact on the resultant model-independent price bounds.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 3.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper relies heavily on advanced mathematical framework around martingale optimal transport and probability theory to establish model-independent bounds. While it provides strong theoretical insights and stylized numerical examples, it lacks empirical validation using actual historical market data.
Research Flowchart
flowchart TD
A[Research Goal: Assess impact of intermediate marginals on Martingale Optimal Transport bounds] --> B[Inputs: Payoff functions, call option prices & initial/final marginals]
B --> C[Incorporate additional intermediate maturity marginals]
C --> D[Analyze MOT duality & characterize market settings for price bounds]
D --> E[Outcome: Conditions for improved vs. unchanged price bounds]
D --> F[Outcome: Numerical examples showing significant tightening of bounds]