Pricing models and analysis of corporate coupon-bonds and credit default swaptions

In this work, pricing models of corporate coupon-bonds and credit default swaptions are derivedand analyzed. Corporate coupon-bonds are priced incorporating both intensity models and structural models, and also jumps introduced by seasonal effects. In deriving the models, we form portfolios to hedge the risk incurred by the instruments, then derive PDE equations using the arbitrage principle and the Ito Lemma for jump processes. The mathematical models are the parabolic-type PDE equations with terminal conditions and boundary conditions. These PDE problems are analyzed and solved by various transformations and incorporation with probabilistic properties. Either a unique solution in the exponential form is obtained, or a particular solution in the separation formis acquired. Further, the pricing model of credit default swaptions is derived using the pricing of corporate coupon-bonds in the similar manner. The main idea of deriving the price of credit default swaptions is to use the price of existing products, i.e., corporate bonds, as opposed to the existing models, which use non-existing forward credit default swap price of the reference entity. The prices of corporate coupon-bonds and credit default swaptions with unexpected default, obtained from these models, are compared to the actual market prices and analyzed