Valuation of Exotic Options and Counterparty Games Based on Conditional Diffusion

Paper: arXiv 2509.13374

Authors: Helin Zhao, Junchi Shen

Abstract

This paper addresses the challenges of pricing exotic options and structured products, which traditional models often fail to handle due to their inability to capture real-world market phenomena like fat-tailed distributions and volatility clustering. We introduce a Diffusion-Conditional Probability Model (DDPM) to generate more realistic price paths. Our method incorporates a composite loss function with financial-specific features, and we propose a P-Q dynamic game framework for evaluating the model’s economic value through adversarial backtesting. Static validation shows our P-model effectively matches market mean and volatility. In dynamic games, it demonstrates significantly higher profitability than a traditional Monte Carlo-based model for European and Asian options. However, the model shows limitations in pricing products highly sensitive to extreme events, such as snowballs and accumulators, because it tends to underestimate tail risks. The study concludes that diffusion models hold significant potential for enhancing pricing accuracy, though further research is needed to improve their ability to model extreme market risks.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel application of conditional Denoising Diffusion Probabilistic Models (DDPMs) with custom financial loss functions for path generation and derivative pricing. It innovates by evaluating the economic value of generated paths using an adversarial P-Q dynamic game framework against traditional models, while honestly addressing its performance limitations on extreme tail-risk products like snowballs.

Research Flowchart

  flowchart TD
    A[Goal: Enhance Exotic Option Pricing & Address Tail Risk] --> B[Input: Financial Market Data & Features]
    B --> C[Method: Train Conditional DDPM Model with Composite Loss]
    C --> D[P-Q Dynamic Game & Adversarial Backtesting vs Monte Carlo]
    D --> E[Outcome 1: Superior Profitability for European & Asian Options]
    D --> F[Outcome 2: Underestimates Tail Risk in Snowballs & Accumulators]