Pricing credit risk through equity options calibration: Part 1 – theory
Marco Fabio Delzio
Purpose – To propose a new methodology to infer the risk-neutral default probability curve of a generic firm XYZ from equity options prices. Design/methodology/approach – It is assumed that the market is arbitrage-free and the “market” probability measure implied in the equity options prices to the pricing of credit risky assets is applied. First, the equity probability density function of XYZ is inferred from a set of quoted equity options with different strikes and maturities. This function is then transformed into the probability density function of the XYZ assets and the term structure of the “option implied” XYZ default probabilities is calculated. These default probabilities can be used to price corporate bonds and, more generally, single-name credit derivatives as “exotic” equity derivatives. Findings – Equity derivatives and credit derivatives have ultimately the same (unobservable) underlying, the XYZ assets value. A model that considers any security issued by XYZ as derivatives on the firm's assets can be used to price these securities in a consistent way to each other and/or detect relative/value opportunities. Originality/value – The paper offers both a pricing tool for traded single-name credit risky assets or a relative value tool in liquid markets.
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