In order to detect mispricings between equity and debt instruments referring to the same company, a mathematical model to jointly evaluate both bonds and stock derivatives is required. These so-called credit-equity models are typically not taught at universities in standard lectures on financial mathematics. The present article provides some insights into the mechanics of such models and highlights arising mathematical difficulties.

Based on the general idea of considering the stock price as the sum over all future expected discounted dividends, a very flexible approach for the modeling of discrete cash dividends is developed. From a theoretical perspective, such a viewpoint automatically implies an arbitrage-free modeling approach and allows for embedding almost any kind of stochastic process and dividend specification. The practical implications are discussed and a tractable pricing framework is presented. Finally, the generic framework is applied to the setup of a defaultable Markov diffusion to highlight the impact of different dividend specifications.

In the post-crisis derivative pricing literature one often finds the statement that the pricing of a collateralized derivative is the same as the pricing of its uncollateralized counterpart, only with adjusted discount factors. We re-derive this statement in the particular case of a CDS by a cashflow-oriented approach, emphasizing the hidden assumptions underlying this derivation. In particular, said pricing technique completely ignores counterparty credit risk and - if more than one currency is involved - necessarily relies on the assumption of funding-dependent discounting. If collateral is posted, the interest rate that has to be paid on the collateral dictates the choice of discounting curve.