Modeling of CDO Options with Multi-Period Spread Dynamics

This paper provides a multi-period extension of the Market Model for forward-start options written on standardized CDS Index Tranches, presented by DORN (2007). Standardized CDS Index Tranches are tranches which securitize CDS index series and dispose of predefined subordination.The central idea consists in defining the forward Fair Tranche Spread as a function of the numeraire used in a Black amp; Scholes closed-form market formula. Hence it becomes possible to select any martingale dynamics for the forward spread rate under the associated probability and one can derive a multi-period dynamics of the forward Fair Tranche Spread for any forward-time horizons. This model is useful for pricing options on tranches with future Issue Dates as well as for modeling emerging options on credit derivatives which include structural enhancements like combo, step-up, or ratio indexed coupon clauses. It becomes also possible to calibrate Index Tranche Options with bespoke tenors/tranche subordination to market data obtained by more liquid Index Tranche Options with standard characteristics