Correlation Skew: A Black-Scholes Approach

Abstract

In this chapter, we view the valuation of CDO tranches as an option pricing problem. The payoff of a CDO tranche is a call-spread on the loss variable. By specifying the distribution of the loss variable at each time horizon, one would be able to value tranches. The standard way of defining this distribution is the base correlation approach. Here, we use a Black-Scholes analogy and we define an implied volatility for each tranche. Then, given a Black volatility surface, we parameterize the loss distribution with a Stochastic CEV model. We show that this parametric form gives a very good fit to the market tranche quotes. In addition, we give an application of the correlation skew Black approach to risk management and hedging.