Paper: arXiv 2409.00095

Authors: Rohini Kumar, Frederick “Forrest” Miller, Hussein Nasralah, Stephan Sturm

Abstract

This paper studies the pricing of contingent claims of American style, using indifference pricing by fully dynamic convex risk measures. We provide a general definition of risk-indifference prices for buyers and sellers in continuous time, in a setting where buyer and seller have potentially different information, and show that these definitions are consistent with no-arbitrage principles. Specifying to stochastic volatility models, we characterize indifference prices via solutions of Backward Stochastic Differential Equations reflected at Backward Stochastic Differential Equations and show that this characterization provides a basis for the implementation of numerical methods using deep learning.

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 presents a rigorous theoretical framework using BSDE-R-BSDEs for American option indifference pricing under dynamic convex risk measures with deep learning applications. While highly advanced mathematically and conceptually original, its empirical validation is strictly numerical and lacks backtesting on real-world market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Risk-Indifference Pricing of American Options] --> B[Inputs: Info Discrepancy & Stochastic Volatility Models]
    B --> C[Method: Indifference Pricing via Dynamic Convex Risk Measures]
    C --> D[Formulation: BSDEs Reflected at BSDEs]
    D --> E[Computation: Deep Learning Numerical Algorithms]
    E --> F[Outcomes: Arbitrage-Consistent Prices & Efficient Solver]