The pricing of structured notes with credit risk

It is inappropriate to ignore counterparty risk when pricing structured products, especially after the financial tsunami that occurred in 2008. Motivated by these circumstances, we developed an exogenous model that embeds the concept of Moody’s KMV model for evaluating the issuer’s credit risk premium under the framework of American binary put option. We select equity-linked structured notes to illustrate that the model is applicable to any kind of financial derivative. The CIR model and GJR-GARCH model are employed to forecast both risk-free rate and variance paths. Fair price under issuer’s credit risk can then be estimated by deducting the premium from the default-free price. The default event can be triggered at any time point and the recovery rate is time-varying, depending on the capital structure of the issuer upon default. Our numerical example shows that the price of a 2-year USD equity-linked note issued by JP Morgan Chase is about 0.9% lower than otherwise identical the default-free note. The default probability within 2 years is 1.8%. Besides, based on the comparative static analysis, the initial asset to debt ratio and asset to strike ratio have a negative effect on default premium, while the asset volatility has a positive effect.

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