Expected RR for name conditinal to default by that date.
Full loss distribution.
This method should be called at the end of non-const methods or when the programmer desires to notify any changes.
Returns the probaility of having a given or larger number of defaults in the basket portfolio at a given time.
Probability of the tranche losing the same or more than the fractional amount given.
The passed lossFraction is a fraction of losses over the tranche notional (not the portfolio).
Probabilities for each of the (remaining) basket elements in the pool to have defaulted by time d and at the same time be the Nth defaulting name to default in the basket. This method is oriented to default order dependent portfolio pricing (e.g. NTDs) The the probabilities ordering in the vector coincides with the pool order.
Saddle point portfolio credit default loss model.
Default Loss model implementing the Saddle point expansion integrations on several default risk metrics. Codepence is dealt through a latent model making the integrals conditional to the latent model factor. Latent variables are integrated indirectly. See: Taking to the saddle by R.Martin, K.Thompson and C.Browne; RISK JUNE 2001; p.91 The saddlepoint method and portfolio optionalities R.Martin in Risk December 2006 VAR: who contributes and how much? R.Martin, K.Thompson and C.Browne RISK AUGUST 2001 Shortfall: Who contributes and how much? R. J. Martin, Credit Suisse January 3, 2007 Don't Fall from the Saddle: the Importance of Higher Moments of Credit Loss Distributions J.Annaert, C.Garcia Joao Batista, J.Lamoot, G.Lanine February 2006, Gent University Analytical techniques for synthetic CDOs and credit default risk measures A. Antonov, S. Mechkovy, and T. Misirpashaevz; NumeriX May 23, 2005 Computation of VaR and VaR contribution in the Vasicek portfolio credit loss model: a comparative study X.Huang, C.W.Oosterlee, M.Mesters Journal of Credit Risk (75-96) Volume 3/ Number 3, Fall 2007 Higher-order saddlepoint approximations in the Vasicek portfolio credit loss model X.Huang, C.W.Oosterlee, M.Mesters Journal of Computational Finance (93-113) Volume 11/Number 1, Fall 2007 While more expensive, a high order expansion is used here; see the paper by Antonov et al for the terms retained. For a discussion of an alternative to fix the error at low loss levels (more relevant to pricing than risk metrics) see: The hybrid saddlepoint method for credit portfolios by A.Owen, A.McLeod and K.Thompson; in Risk, August 2009. This is not implemented here though (yet?...) For the more general context mathematical theory see: Saddlepoint approximations with applications by R.W. Butler, Cambridge series in statistical and probabilistic mathematics. 2007
Some portfolios show instabilities in the high order expansion terms.
Methods here are calling and integrating using the unconditional probabilities without inverting them first; quite a lot of calls to the copula inversion can be avoided; this should improve performance.
Revise the model for stability of the saddle point calculation. The search for the point does not convege in extreme cases; e.g. very high value of all the factors; factors for each variable not ordered from high to low,...
The treatment of recovery wont work with random recoveries, they should be passed to the conditional methods in the same way as the probabilities.
TO DO: Failing when the tranche upper loss limit goes over the max attainable loss.
(over region around the EL I think)ProbDef = 0 thereWhen introducing defaults; somewhere, (after an update?) there should be a check that: copula_->basketSize() EQUALS remainingBasket_.size()