Convertible Bonds Pricing Analytics

A quantitative finance repository focused on convertible bond pricing and risk analytics.

This project develops a jump-diffusion pricing framework for convertible bonds, combining equity risk, credit risk, and deterministic interest-rate discounting within a PDE-based approach.

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Repository Structure

Convertible-Bonds-Pricing-Analytics/
├── Convertible Bonds Pricing Analytics.ipynb

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Project Overview

This notebook focuses on the pricing of convertible bonds as hybrid securities combining fixed-income and equity-option features.

It models equity risk through the stock-price dynamics, credit risk through a Poisson default process with deterministic time-varying intensity, and rate risk through a deterministic market yield curve. Within this framework, default leads to a recovery-based payoff, while the conversion feature gives the holder exposure to the upside of the underlying equity. The model also incorporates embedded issuer call features, allowing the analysis of callable convertible structures.

The pricing framework is first developed for a defaultable vanilla bond, based on survival probabilities, default probabilities, and recovery-adjusted discounted cash flows. This credit-sensitive bond layer then serves as the foundation for the broader convertible bond valuation and risk-analysis framework.

Beyond pricing, the notebook also computes risk sensitivities through finite-difference approximations.

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Model Components

The implementation includes:

• Poisson default modelling
• Survival and default probability calculations
• Recovery-based default payoff modelling
• Deterministic defaultable bond pricing
• PDE-based convertible bond pricing
• Embedded conversion and issuer call features
• Finite-difference risk analytics

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Example Output

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Best use case

Use this notebook when working with hybrid credit-equity derivatives and building a convertible bond pricing framework for valuation and risk analysis.

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How to Use

Clone the repository:

git clone https://github.com/Idriss-Afra/Convertible-Bonds-Pricing-Analytics.git
cd Convertible-Bonds-Pricing-Analytics
jupyter notebook

Then open:

• Convertible Bonds Pricing Analytics.ipynb

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Author

Idriss Afra