The Valuation of Option Contracts subject to Counterparty Risk

Abstract

As a result of the global financial crisis, the credit risk of OTC derivatives became a more important issue in finance industry. In contrast to exchange traded markets, OTC markets lack the advantage of a central clearing house ensuring that the counterparties fulfill their obligations. The risk that the promised payments are not made is called counterparty or default risk. Derivatives subject to counterparty risk are called vulnerable derivatives. Since the counterparty risk cannot be ignored, it should be considered in the valuation of OTC derivatives. This dissertation addresses the valuation of European and American options which are traded on OTC markets. Both European and American options exhibit unilateral counterparty risk, since these contracts constitute an obligation only for the option writer. For vulnerable European options, the valuation models of Klein (1996), Klein and Inglis (2001) as well as Liu and Liu (2011) prevail in the literature. Based on an extended Black-Scholes world, they use the structural approach of Merton (1974) to price European options subject to counterparty risk. In this dissertation, these models are combined in a general model which incorporates their key characteristics. Moreover, the mentioned models are extended to a stochastic interest rate framework. In addition, valuation models for vulnerable American options are set up using the core ideas of Klein (1996), Klein and Inglis (2001) as well as Liu and Liu (2011).