Learning to Hedge Swaptions

Code accompanying the paper:

Learning to Hedge Swaptions
Zaniar Ahmadi and Frédéric Godin
Concordia University, Quantact/CRM
November 26, 2025

This repository implements a deep hedging framework for European swaptions based on reinforcement learning.
The code compares deep hedging agents (trained under different risk objectives) with traditional rho-hedging in a three-factor discrete-time arbitrage-free Nelson–Siegel (DTAFNS) model.

The experiments show that:

• Deep hedging achieves multi-period optimal dynamic hedges.
• Using two payer swaps as hedging instruments is essentially near-optimal in this setting.
• Different risk objectives (MSE, downside risk, CVaR) lead to distinct hedging styles and trade-offs between tracking error, downside risk, and tail protection.

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1. Repository structure

learning-to-hedge-swaptions/
├── src/
│   ├── config.py
│   ├── main.py
│   ├── training.py
│   ├── pricing.py
│   ├── networks.py
│   ├── data_generation.py
│   ├── utils.py
│   ├── evaluation.py
│   ├── DTAFNSModels.py
│   ├── DTAFNS_model_forward_measure.py
│   ├── DTAFNS_zero_coupon_price_multipaths.py
│   ├── DTAFNS_swaption_pricing_forward.py
│   ├── DTAFNS_swap_pricing_forward.py
│   └── __init__.py
├── models/
│   └── pretrained/
│           └──  swaption_network_al60_be180_k25083_forgrad_fastkan.pth
├── docs/
│   └── Learning_to_Hedge_Swaptions.pdf
├── README.md
├── .gitignore
└── requirements.txt

Main components

DTAFNSModels.py, DTAFNS_model_forward_measure.py, DTAFNS_zero_coupon_price_multipaths.py, DTAFNS_swaption_pricing_forward.py, DTAFNS_swap_pricing_forward.py : Implementation of the discrete-time arbitrage-free Nelson–Siegel model (DTAFNS), zero-coupon bond pricing, swap and swaption pricing, and measure changes (risk-neutral and forward measures).

data_generation.py : Configuration and scripts to simulate factor paths and generate Monte Carlo datasets (term-structure states, swaption payoffs, hedging features).

pricing.py, networks.py : Implementation and training of the Kolmogorov–Arnold Network (KAN) used as a fast swaption pricing surrogate (“deep pricer”) and its sensitivities (rhos). The file models/swaption_network_al60_be180_k25083_forgrad_fastkan.pth stores a trained FastKAN swaption pricing network.

training.py, main.py : Training loop for deep hedging agents:

State: yield-curve factors, time-to-maturity, and current portfolio value.

Action: hedge ratios in one, two, or three payer swaps.

Objective: MSE, downside risk, or CVaR of the terminal hedging error.

Optimization via stochastic gradient descent / Adam.

evaluation.py : Scripts to compute and report the hedging performance metrics on out-of-sample paths:

Mean hedging error

RMSE and root downside risk

CVaR

Probability of under-hedging

Hedging Risk Reduction (HRR)

Trading Intensity (TI)

Dynamic Tracking Error (DTE)

config.py, utils.py : Configuration utilities, common helper functions, and potentially simple CLI options for running the different experiments.

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Installation

Follow the steps below to set up the environment and run the project.

1. Clone the repository

git clone https://github.com/zaniara3/learning-to-hedge-swaptions.git
cd learning-to-hedge-swaptions

2. Create and activate a virtual environment (recommended)

macOS / Linux

python3 -m venv .venv
source .venv/bin/activate

Windows (PowerShell)

python -m venv .venv
.venv\Scripts\activate

3. Install the required Python packages

pip install -r requirements.txt