  We performed a comprehensive analysis on the price bounds of CDO tranche
options, and illustrated that the CDO tranche option prices can be effectively
bounded by the joint distribution of default time (JDDT) from a default time
copula. Systemic and idiosyncratic factors beyond the JDDT only contribute a
limited amount of pricing uncertainty. The price bounds of tranche option
derived from a default time copula are often very narrow, especially for the
senior part of the capital structure where there is the most market interests
for tranche options. The tranche option bounds from a default time copula can
often be computed semi-analytically without Monte Carlo simulation, therefore
it is feasible and practical to price and risk manage senior CDO tranche
options using the price bounds from a default time copula only.
  CDO tranche option pricing is important in a number of practical situations
such as counterparty, gap or liquidation risk; the methodology described in
this paper can be very useful in the above described situations.
