On the entropy minimal martingale measure in the exponential Ornstein-Uhlenbeck stochastic volatility model

Paper: arXiv 2501.02396

Authors: Yuri Kabanov, Mikhail A. Sonin

Abstract

We consider a stochastic volatility model where the price evolution depend on the exponential of the Ornstein–Uhlenbeck process. After a brief revision of the related theory the entropy-minimal equivalent martingale measure. is calculated.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical derivation of the entropy-minimal equivalent martingale measure for an exponential Ornstein-Uhlenbeck stochastic volatility model. However, its empirical validation is extremely weak, relying on arbitrarily selected parameter values rather than formal calibration to market data.

Research Flowchart

  flowchart TD
    A[Goal: Find Entropy-Minimal Equivalent Martingale Measure] --> B[Input: Asset Price & Exp-OU Volatility Model]
    B --> C[Review Stochastic Volatility & Martingale Theory]
    C --> D[Apply Girsanov Theorem & Entropy Minimization]
    D --> E[Solve Dual Optimization Problem]
    E --> F[Outcome: Explicit Formula for Minimal Entropy Measure]
    F --> G[Application: Derivatives Pricing under MEMM]