A Unified Framework for Pricing Credit and Equity Derivatives

TL;DR

This paper introduces a unified model that jointly calibrates to corporate bond and equity option markets, enabling accurate pricing of derivatives and capturing market-observed credit spreads and volatility surfaces.

Contribution

The paper presents a novel risk-neutral framework that simultaneously fits bond and equity option data, improving pricing accuracy for complex derivatives.

Findings

Model matches market CDS spreads without direct calibration.

Accurately reproduces equity implied volatility surface.

Highlights importance of default risk and stochastic interest rates.

Abstract

We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid or over-the-counter derivatives. We observe that the model implied credit default swap (CDS) spread matches the market CDS spread and that our model produces a very desirable CDS spread term structure. This is observation is worth noticing since without calibrating any parameter to the CDS spread data, it is matched by the CDS spread that our model generates using the available information from the equity options and corporate bond markets. We also observe that our model matches the equity option implied volatility surface well since we properly account for the default risk premium in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque, Papanicolaou, Sircar and Solna (2003), which only accounts for stochastic volatility.