This title slide presents a "Heston Model Snowball Option Pricing System Based on Differential Deep Learning" in Chinese. The subtitle reads "Technical Summary Report."

基于微分深度学习

Heston 模型雪球期权定价系统

技术总结汇报

Source: 技术总结汇报

This agenda slide outlines the presentation structure, beginning with project core objectives (background, pain points, solutions, results). It then covers data construction (models, sampling, labels, scale), feature engineering, neural network architecture, training strategies, and final performance validation (speed, accuracy, robustness).

汇报议程

1. 项目核心目标

背景、痛点、解决方案、成果

2. 数据构造模块

模型、采样、标签、规模

3. 特征工程

输入特征、逻辑、预处理

4. 神经网络架构

结构、激活函数、设计思路

5. 训练策略

损失函数、导数约束、优化器

6. 最终表现与验证

速度、精度、鲁棒性

The slide outlines the background and pain points of traditional Heston model snowball option pricing, which is complex and relies on slow, unstable Monte Carlo simulations unable to meet real-time needs. It proposes a solution using differential deep learning combined with PDE methods to build an efficient pricing system for fast, accurate calculations.

1. 项目核心目标

The Data Construction Module workflow defines the Heston model with stochastic volatility parameters (κ, θ, σv, ρ, v0), simulates 1 million paths via Monte Carlo, and generates labels using precise BSDE solutions for option true prices. The dataset is then split into 500k training samples and 100k testing samples.

2. 数据构造模块

{ "headers": [ "步骤", "描述", "关键参数" ], "rows": [ [ "Heston模型定义", "随机波动率模型参数设置", "κ, θ, σv, ρ, v0 等" ], [ "路径模拟", "蒙特卡洛模拟生成路径", "10^6 条路径" ], [ "标签生成", "精确BSDE求解计算标签", "期权真实价格" ], [ "数据集划分", "训练/测试集拆分", "训练50万，测试10万" ] ] }

This slide on Feature Engineering lists core inputs (price, volatility, rates, barriers) alongside preprocessing steps like time standardization, log volatility transform, normalization, and noise injection. These techniques ensure consistent scaling, stable distributions, and enhanced model robustness.

3. 特征工程

{ "features": [ { "icon": "📊", "heading": "Core Input Features", "description": "Initial price, volatility, interest rate, knock-in/out barriers." }, { "icon": "⏱️", "heading": "Time Standardization", "description": "Normalizes time dimensions for consistent model input scaling." }, { "icon": "🔢", "heading": "Log Volatility Transform", "description": "Applies logarithm to volatility for stable distributions." }, { "icon": "📏", "heading": "Feature Normalization", "description": "Scales inputs to zero mean and unit variance." }, { "icon": "🎲", "heading": "Noise Injection", "description": "Adds controlled Gaussian noise to enhance robustness." } ] }

The slide describes the DGM neural network architecture, featuring 8 fully connected layers with Swish activation for smooth differentiability. It incorporates a physics-informed design that embeds PDE constraints and effectively handles high-dimensional inputs.

4. 神经网络架构

!Image

• DGM architecture: 8 fully connected layers structure.
• Activation function: Swish for smooth differentiability.
• Physics-informed design embeds PDE constraints.
• Supports high-dimensional input processing effectively.

Source: Image from Wikipedia article "Physics-informed neural networks"

The training strategy uses MSE loss combined with derivative constraints, leveraging automatic differentiation of PDE residuals. It employs the AdamW optimizer with a learning rate of 1e-4 and batch size of 512.

5. 训练策略

• MSE loss + derivative constraints
• Automatic differentiation of PDE residuals
• AdamW optimizer: LR=1e-4, batch=512

The slide showcases a 20x speed boost over MC alongside RMSE pricing errors under 0.5%. It also reports excellent robustness and generalization under parameter perturbations on stable test sets.

6. 最终表现与验证

• 20x: 比MC快

速度提升20倍

• <0.5%: RMSE精度

定价误差极低

• 优异: 鲁棒性与泛化

参数扰动稳定测试集优秀

The slide summarizes the system's efficient pricing of Heston snowball options and outlines future extensions to multi-assets. It concludes with thanks for listening and an invitation for Q&A.

总结与展望

系统高效定价 Heston 雪球期权 未来扩展多资产

感谢聆听！Q&A

Source: Heston雪球期权定价系统