2009/12/15 by Damiano Brigo, Brigo, Damiano, Marco Tarenghi +1
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #Credit Risk and Financial Regulations #FOS: Economics and business #Pricing of Securities (q-fin.PR) #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.0912.3031
Revised version included in D. Brigo, M. Morini, Structural credit calibration, 2006, Risk Magazine, April issue
arxiv created 2009/12/15 · openalex publication_date 2009/12/15 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we develop a tractable structural model with analytical default probabilities depending on a random default barrier and possibly random volatility ideally associated with a scenario based underlying firm debt. We show how to calibrate this model using a chosen number of reference Credit Default Swap (CDS) market quotes. In general this model can be seen as a possible extension of the time-varying AT1P model in Brigo and Tarenghi (2004). The calibration capability of the Scenario Volatility/Barrier model (SVBAT1P), when keeping time-constant volatility, appears inferior to the one of AT1P with time-varying deterministic volatility. The SVBAT1P model, however, maintains the benefits of time-homogeneity and can lead to satisfactory calibration results, as we show in a case study where we compare different choices on scenarios and parameters. Similarly to AT1P, SVBAT1P is suited to pricing hybrid equity/credit derivatives and to evaluate counterparty risk in equity payoffs, and more generally to evaluate hybrid credit/equity payoffs. We consider the equity return swap in Brigo and Tarenghi (2004) and show its valuation under SVBAT1P with the same CDS and equity calibration input used earlier for AT1P, and further we hint at equity default swap valuation in the conclusions.