Credit derivatives have attracted much attention in recent years. A number of models have been developed aimed at the pricing of these instruments. In this paper, we offer a framework for modelling risky debt and valuing credit derivatives that is flexible and simple to implement, and that is, to the maximum extent possible, based on observables. We utilise the risk0neutral pricing methodology, providing an arbitrage0free model for valuing credit derivatives.
Two distinct approaches are visible in the literature to the modelling of credit risk. One, following the lead of Merton [34], views debt as a contingent claim written on the assets on the firm. The typical model here posits a process for the evolution of firm value, and specifies the conditions leading to bankruptcy as well as the payoffs to various parties in the event of bankruptcy. The value of debt is then derived as a consequence.
Risk about future payoffs is at the center of asset pricing, asset allocation, and option pricing. Prices at the stock and bond market, and in particular option prices, can react significantly to a change in uncertainty. Over the last years, the VIX volatility index, which is the square-root of a model-free variance calculated from the cross-section of SPX option prices, became a well-known measure for uncertainty. In the financial crises, the VIX, which has usually been around 20%, has exceeded the level of 80% several times. During this time, but also during former periods of market stress like the stock market crash of 1987, or the collapse of LTCM, volatility derivatives, which allow to trade variance risk, thus naturally attracted attention.
In the modern environment of radically enhanced global macroeconomic and financial link-ages, isolated country analysis seems highly insufficient for informed assessment of the state of real activity, and hence for informed decision making. In this paper, we propose and implement a framework for characterizing and monitoring the global business cycle. The framework is informed by economic theory and structured so as to help inform subsequent economic theory. We apply it to the G-7 countries, and in so doing we extend the empirical research program on the global business cycle along several dimensions.
First, we consider the roles played by a large set of macroeconomic indicators when we construct our country and global cycles. The country and global factors that we estimate provide a better characterization of business cycles as they encompass a wide array of activity measures, in the tradition of Burns and Mitchell (1946) and much subsequent research. This contrasts with most of the literature on global business cycles, which uses only quarterly national income and product account data.
