Measuring distribution risk in discrete models

Paper: arXiv 2302.08838

Authors: Roberto Fontana, Patrizia Semeraro

Abstract

Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of choosing a risk-neutral measure on convex derivative pricing in incomplete markets. We find analytical bounds for prices of European and American options in the class of all risk-neutral measures, and we also find simulated bounds for given classes of perturbations of the minimal martingale equivalent measure.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical framework for model risk and distribution risk using discrete models and martingale measures. However, it relies heavily on theoretical bounds and simulations rather than rigorous empirical backtesting with real market data.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Quantify model & distribution risk<br>in incomplete markets"] --> B["Inputs:<br>Discrete market model,<br>convex derivative payoffs<br>& minimal martingale measure"]
    
    B --> C["Methodology:<br>Analyze class of all equivalent<br>risk-neutral measures & perturbations"]
    
    C --> D["Computational Process:<br>Derive analytical bounds &<br>run simulations for option pricing"]
    
    D --> E1["Outcome 1:<br>Analytical price bounds for<br>European & American options"]
    D --> E2["Outcome 2:<br>Simulated risk bounds under<br>perturbed martingale measures"]