The thesis consists of two major parts, and it contributes to two topics in risk models - a dynamic model of central counterparty risk and... Show moreThe thesis consists of two major parts, and it contributes to two topics in risk models - a dynamic model of central counterparty risk and liquidity risk measures.Chapter 2 is devoted to the first part of the thesis, where we propose a dynamic model of central counterparty risk by introducing a dynamic model of the default waterfall of derivatives Central Counterparties (CCPs) and by designing a risk sensitive method for sizing the initial margin (IM), and the default fund (DF) and its allocation among clearing members. Using a Markovian structure model of joint credit migrations, our evaluation of DF takes into account the joint credit quality of clearing members as they evolve over time. Another important aspect of the proposed methodology is the use of the time consistent dynamic risk measures for computation of IM and DF. We carry out a comprehensive numerical study, where, in particular, we analyze the advantages of the proposed methodology and its comparison with the currently prevailing methods used in industry. The second part of the thesis is divided into four chapters, and the primary goal of this part is to develop a general framework for liquidity risk management in an order driven market. Chapter 3 describes the essential elements of an order driven market and introduces the notions that are of critical financial meaning, for instance, trading strategy and its corresponding value process. Moreover, we propose a model for the dynamics of the limit order book by using marked point process. Chapter 4 is devoted to the identification and measurement of liquidity risk. We describe the importance of demand for liquidity in measuring liquidity risk and we introduce the concept of liquidity provision. By considering a trader who is subject to liquidity provision only, we demonstrate that liquidity provision impacts the valuation of the portfolio through the trading costs of the foreseen transactions. Then, we propose two portfolio liquidity risk measures to account for the liquidity risk introduced by the liquidity provision. Besides measuring the liquidity risk of a portfolio, we also design a method to measure the liquidity provision adjusted risk for any contingent claim in the financial market established in Chapter 3. Chapter 5 attends to the hedging problem under liquidity provision. We prove the existence of an optimal hedging strategy in terms of minimizing the hedging error under liquidity provision. We demonstrate that the optimal hedging strategy can be solved in terms of associated Bellman equations. Show less
