The thesis intends to lay down innovative foundations for valuing contracts or portfolios of contracts under counterparty risk and in the presence of netting agreements. The approach departs from the usual methods for pricing contracts, and portfolios of contracts, with counterparty risk found in the literature. In effect, typically, these models, first, do not account for either systemic effects or 'at first default' contagion, second, postulate that the contract value at default equals either the default-free value or the pre-default value, and third, do not take margin agreements into account. Instead, we propose a general framework which allows for examining the bilateral counterparty risk of a contract, or a portfolio of contracts, in the presence of systemic and 'right or wrong way' risks, and under several settlement conventions, possibly with netting, and margin agreements. The methodology, which has been designed to cover a large class of financial instruments, is illustrated by means of numerous examples, such as an interest rate swap, a credit default swap, a collateralized debt obligation, and a credit index. In effect, suitable extensions of Kusuoka's models are constructed in order to present the approach as well as analyse the specifics of valuation and hedging under counterparty risk. The results are then leveraged so as to build an efficient and versatile model for pricing under counterparty risk, namely an affine Markov chain model which accounts for settlement convention, dependency of times of default, contagion effect at first default, right or wrong way risk, collateralization and systemic risk. Let us also emphasize that the pricing procedures are presented in detail, which should give readily implementable pricing algorithms for practitioners.
