Credit barrier models.

Description

The thesis contains the construction of a new class of pricing models for credit derivatives. The underlying stochastic process models the credit quality of individual obligors within the wider context of all firms that issue debt. The challenge is to reconcile a broad set of statistical and pricing information within a model where the main observables can be computed as integrals or sums of well-known functions, and the other observables are obtainable through efficient numerical schemes.Lastly, we give applications of this credit model. Risk-neutral transition probabilities are calculated and compared with those calculated using previous models. Credit default swaps are priced. A mapping to equity in which the equity process is a martingale is constructed. This mapping to equity allows us to price, in particular, equity default swaps. Empirical results from the mapping indicate that the constant elasticity of variance (CEV) process would be an appropriate pure diffusion approximation to our process to price equity default swaps, and results using the CEV process are presented.In the first part, we use continuous processes that are based on square-root diffusion processes. Parameterized local volatility is introduced by a measure change and a coordinate transformation in such a way that the stochastic process retains integrability. Jumps in the process are introduced by subordinating on a random time-change. With this framework we are able to match empirical data on credit processes. Adding a drift enables us to introduce a measure change to the pricing measure to achieve consistency with market prices.In the second part, we discretise the stochastic process in such a way that node-to-node transition probabilities can be computed as sums of orthogonal polynomials. In this way, computing efficiency is increased while the empirical properties of the model remain intact.

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