Valuation Bound of Tranche Options

TL;DR

This paper establishes narrow price bounds for CDO tranche options using a default time copula, enabling practical and semi-analytical pricing and risk management especially for senior tranches.

Contribution

It introduces a method to bound tranche option prices with a default time copula, reducing reliance on extensive simulations and highlighting limited impact of systemic factors.

Findings

Price bounds are often very narrow for senior tranches.

Default time copula can be used for semi-analytical pricing.

Systemic and idiosyncratic factors contribute limited pricing uncertainty.

Abstract

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.