Currency Crashes, Tail Risk and Contingent Capital

Abstract

This thesis studies currency crashes and risk premia from the perspective of options, as well as the pricing of Contingent Convertible Bonds (CoCo).

In the first part, we set up an arbitrage-free time-changed Levy model inspired by Carr and Wu (2004) which generates yield curves and exchange rate dynamics consistent with currency option prices in G10 countries. In this framework, we investigate the pricing of cross-pair G10 currency options, and construct estimates of conditional currency risk premia at each point in time in our sample from January 1999 to June 2012. We discover the option-implied currency risk premia are not distinguishable from their realized counterpart, suggesting the realized returns do not suffer from peso problems. We also decompose the total risk premium into their contributions from variance and higher order cumulants, and discover the higher cumulants' contribution

merely represents 15% of the total risk premium.

In the second part, we study a typical hybrid instrument (CoCo) designed to

relieve banks from the pressure of raising new capital during crisis periods. CoCos convert into equities upon a contractual trigger event, and are exposed to different sources of risk: interest rate risk, equity risk and conversion risk. We develop a general framework for their pricing and hedging that can be specified in different ways. We focus on reduced-form and structural models driven by a finite-dimensional Markov process. But both allow to price CoCos and calculate dynamic hedging strategies with holdings in related instruments such as fixed income products, the issuing company's

stock and credit default swaps. We conclude the the study of CoCo's with a discussion on several issues in its design using the framework of Leland's model (1996).