| This thesis consists of three essays about modeling counterparty risk and pricing derivative securities.;In the first essay, we analyze the counterparty risk embedded in CDS contracts, in presence of a bilateral margin agreement. We focus on the pricing of collateralized counterparty risk, and we derive the Credit Valuation Adjustment (CVA). We propose a model for the collateral by incorporating all related factors such as the thresholds, haircuts and margin period of risk. We derive the dynamics of the bilateral CVA in a general form with related jump martingales. We introduce Spread Valuation Adjustment (SVA) which accounts for the counterparty risk in CDS spreads. We finally employ a Markovian copula model to illustrate our findings.;In the second essay, we address the issue of computation of the CVA under rating triggers in presence of ratings-linked margin agreements. We consider collateralized OTC contracts, that are subject to rating triggers, between two counterparties. We model the margin process as a function of the credit ratings of the counterparties. We employ a Markovian approach for modeling of the rating transitions and of the default probabilities of the counterparties. In this framework, we introduce the rating valuation adjustment (RVA) that accounts for the rating triggers. We consider several dynamic collateralization schemes where the margin thresholds are linked to the credit ratings of the counterparties. We account for the rehypothecation risk in the presence of independent amounts. Our results are illustrated in terms of a CDS contract and an IRS contract.;In the third essay, we study the problem of pricing in incomplete markets with risk measures and acceptability indices. We propose a model for finding the dynamic ask and bid prices of derivative securities using Dynamic Coherent Acceptability Indices (DCAI) in the presence of transaction costs. In this framework, we define and prove a representation theorem for dynamic bid ask prices. We show that our prices can be computed using dynamic Gain-Loss Ratio. To illustrate our results, we provide several numerical examples, by pricing barrier options with dGLR. |
