FAILURE OF SADDLE-POINT METHOD IN THE PRESENCE OF DOUBLE DEFAULTS

We show that the saddle-point approximation method to quantify the impact of undiversi?ed idiosyncratic risk in a credit portfolio is inappropriate in the presence of double default effects. Speci?cally, we prove that there does not exist an equivalent formula to the granularity adjustment, that accounts for guarantees, in case of the extended single-factor CreditRisk+ model. Moreover, in case of the model underlying the double default treatment within the internal ratings based (IRB) approach of Basel II, the saddle-point equivalent to the GA is too complex and involved to be competitive to a standard Monte Carlo approach.analytical approximation, Basel II, double default, granularity adjustment, IRB approach, saddle- point approximation

An asymptotic expansion for a Black–Scholes type model

AbstractWe consider the Black–Scholes model where we add a perturbation term ∑iεiσi to the model with diffusion coefficient σ0(t). Then we derive an asymptotic expansion for the expected value of an European call option at time t. This is done by applying methods of Malliavin calculus. Borel summability of the derived asymptotic expansion is proven

Treatment of Double Default Effects within the Granularity Adjustment for Basel II

Within the Internal Ratings-Based (IRB) approach of Basel II it is assumed that idiosyncratic risk has been fully diversi?ed away. The impact of undiversi?ed idiosyncratic risk on portfolio Value-at-Risk can be quanti?ed via a granularity adjustment (GA). We provide an analytic formula for the GA in an extended single- factor CreditRisk+ setting incorporating double default e?ects. It accounts for guarantees and their e?ect of reducing credit risk in the portfolio. Our general GA very well suits for application under Pillar 2 of Basel II as the data inputs are drawn from quantities already required for the calculation of IRB capital charges.analytic approximation, Basel II, counterparty risk, double default, granularity adjustment, IRB approach, securitization

Funding Liquidity, Debt Tenor Structure, and Creditor's Belief: An Exogenous Dynamic Debt Run Model

We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. At rollover dates of short-term debt, creditors face a dynamic coordination problem. We show that a unique threshold strategy (i.e., a debt run barrier) exists for short-term creditors to decide when to withdraw their funding, and this strategy is closely related to the solution of a non-standard optimal stopping time problem with control constraints. We decompose the total credit risk into an insolvency component and an illiquidity component based on such an endogenous debt run barrier together with an exogenous insolvency barrier.Comment: 36 pages, 9 figures. The article was previously circulated under the title A Continuous Time Structural Model for Insolvency, Recovery, and Rollover Risks in Mathematics and Financial Economics, 201

Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

We show how inter-asset dependence information derived from observed market prices of liquidly traded options can lead to improved model-free price bounds for multi-asset derivatives. Depending on the type of the observed liquidly traded option, we either extract correlation information or we derive restrictions on the set of admissible copulas that capture the inter-asset dependencies. To compute the resultant price bounds for some multi-asset options of interest, we apply a modified martingale optimal transport approach. In particular, we derive an adjusted pricing-hedging duality. Several examples based on simulated and real market data illustrate the improvement of the obtained price bounds and thus provide evidence for the relevance and tractability of our approach

Improved Modeling of Double Default Effects in Basel II - An Endogenous Asset Drop Model without Additional Correlation

In 2005 the Internal Ratings Based (IRB) approach of `Basel II' was enhanced by a `treatment of double default effects' to account for credit risk mitigation techniques such as ordinary guarantees or credit derivatives. This paper reveals several severe problems of this approach and presents a new method to account for double default effects. This new it asset drop technique can be applied within any structural model of portfolio credit risk. When formulated within the IRB approach of Basel II, it is very well suited for practical application as it does not pose extensive data requirements and economic capital can still be computedBasel II, double default, IRB approach, regulatory capital, structural credit portfolio models