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TOPICS IN COUNTERPARTY RISK AND DYNAMIC CONIC FINANCE
Title
TOPICS IN COUNTERPARTY RISK AND DYNAMIC CONIC FINANCE
Creator
Iyigunler, Ismail
Date
2012-11-02, 2012-12
Description
This thesis consists of three essays about modeling counterparty risk and pricing derivative securities. In the rst essay, we analyze the...
Show moreThis thesis consists of three essays about modeling counterparty risk and pricing derivative securities. In the rst 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 bilateral Credit Valuation Adjustment (CVA), unilateral Credit Valuation Adjustment (UCVA), and Debt Valuation Adjustment (DVA). 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. Counterparty risky and the counterparty risk-free spread dynamics are derived and the dynamics of the Spread Value Adjustment (SVA) is found as a consequence. We nally employ a Markovian copula model for default intensities and illustrate our ndings with numerical results. In the second essay we address the issue of computation of the bilateral CVA under rating triggers in presence of ratings-linked margin agreements. We consider collateralized OTC contracts, that are subject to rating triggers, between two parties { an investor and a counterparty. Moreover, we model the margin process as a function of the credit ratings of the counterparty and the investor. We employ a Markovian approach for modeling of the rating transitions and of the default probabilities of the counterparties. In this framework, we derive the representation for bilateral CVA. We also introduce a new component in the decomposition of the counterparty risky price: namely 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 ix 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 nding 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 de ne and prove a representation theorem for dynamic bid ask prices. We show that our prices can be computed using dynamic Gain-Loss Ratio (dGLR), which is a DCAI. To illustrate our results, we provide several numerical examples, by pricing barrier options with dGLR.
PH.D in Applied Mathematics, December 2012
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