Posts Tagged ‘Probabilidad


¿Completando mercados o timba timba?

Si no me equivoco este producto -CEBO (titulo que se presta al juegos de palabras)- ya estaba, solo que ahora lo relanzan especificando “el evento” como bancarrota. Por su parte, Zero Hedgese preocupa” por el efecto en los modelos actuales.


Paper: Tasas de recuperación

Calibration of Structural and Reduced-Form Recovery Models


In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distribution can be underestimated considerably. The problem of underestimating tail losses becomes even more severe, when calibration issues are taken into account. To demonstrate this we choose a Merton-type structural model as our reference system. Diffusion and jump-diffusion are considered as underlying processes. We run Monte Carlo simulations of this model and calibrate different recovery models to the simulation data. For simplicity, we take the default probabilities directly from the simulation data. We compare a reduced-form model for recoveries with a constant recovery approach. In addition, we consider a functional dependence between recovery rates and default probabilities. This dependence can be derived analytically for the diffusion case. We find that the constant recovery approach drastically and systematically underestimates the tail of the loss distribution. The reduced-form recovery model shows better results, when all simulation data is used for calibration. However, if we restrict the simulation data used for calibration, the results for the reduced-form model deteriorate. We find the most reliable and stable results, when we make use of the functional dependence between recovery rates and default probabilities.

Link al Paper



Gráfico du Jour: Pronósticos

(Fuente: NYT)


Link entre los CDS spreads y las probabilidades de default

Asi se llama un reciente post del blog de Kamakura Corp. De forma inteligente parte de una noticia sobre BP, para elegantemente criticar -y hacer un poco de PR de su método alternativo- el conversor de CDS de ISDA de spread basis a upfront basis.

As Prof. Jarrow describes it, there are two ways to understand the linkages between CDS spreads and default probabilities:

Bottoms up approach: Build a model, assume it’s true, and solve for continuous default probability (“risk neutral”) that matches observable pricing
Top down approach: Determine the factors driving the intersection of supply and demand and use an econometric approach to derive (empirical) default probabilities

The ISDA Standard CDS Converter is a “bottoms up” approach that makes a number of simplifying assumptions, something very much in keeping with the “yield to maturity” analogy:

  • Forward interest rates are step-wise constant, not a smooth continuous curve such as those we have discussed in our many blogs on yield curve smoothing
  • Default intensity, the continuous time probability of default, is constant over the life of the credit default swap contract. Similarly, the yield to maturity formula assumes that interest rates are constant over the life of the bond in question.
  • The only relevant factors to consider are the instantaneous probability of default, the recovery rate, and interest rate levels
  • The counterparty on the CDS contract will not default

There is nothing wrong with this approach–as long as one is aware of its limitations. The yield to maturity formula, for example, is deeply embedded in bond markets but it is well known that it is not best practice for valuation or risk management.  In the same way, the ISDA Standard CDS Converter is embedded in the mechanics of settlement but it is too simple for accurate valuation and risk management.

The reason the ISDA Standard CDS Converter is too simple is that it assumes only three factors affect the link between CDS spreads and default probabilities:

  • Interest rates
  • Recovery rates
  • The constant continuous time default intensity

We now turn to the “top down” approach to show why the ISDA Standard CDS Converter is too simple for accurately describing the links between spreads and default probabilities. Instead of assuming the (ISDA) theory is true, we assume the market data is true and derive insights from it. In this section, we summarize our findings in the RISK 2007 publication and companion blog entry listed above.  For data on default probabilities, we used the then-current reduced form or “Jarrow-Chava” default probabilities from Kamakura Risk Information Services.


Explicando Finanzas Estructuradas

Marginal Revolution le dedica un post a las finanzas estructuradas y a sus dotes de ocultar el riesgo (a.k.a CDO). La breve nota incluye un ejemplo y una hoja de calculo; muy explicativo.


Suppose that we misspecified the underlying probability of mortgage default and we later discover the true probability is not .05 but .06.  In terms of our original mortgages the true default rate is 20 percent higher than we thought–not good but not deadly either.  However, with this small error, the probability of default in the 10 tranche jumps from p=.0282 to p=.0775, a 175% increase.  Moreover, the probability of default of the CDO jumps from p=.0005 to p=.247, a 45,000% increase!


Paper sobre el tema.


Probabilidad y Estadística

Entre el 1 y 3 de Diciembre de 2010, se realizara -en Santa Fe, Argentina- el 7° Encuentro Regional de Probabilidad y Estadística Matemática. Organizado por el Instituto de Matematica Aplicada del Litoral (IMAL, UNL-CONICET) y la Facultad de Ingenieria Quimica (FIQ, UNL).

Para más informacion visite


Fun & Finance


Fun & Finance Rollover

"It is hard to be finite upon an infinite subject, and all subjects are infinite." Herman Melville

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