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CDS and rating announcements: changing signaling during the crisis?

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Abstract

In parallel with the development of credit derivatives market, researchers have begun to explore the relationship between Credit Default Swap (CDS) market and rating events. Many papers, via classical event-study methodology, show that CDS market is able to signal future negative rating events announced by credit rating agencies. In this work, we incorporate into the event-study methodology the ability of Markov switching models in modeling state-dependent means and variances. This approach allows to get over the drawbacks of the classical methodology, which ignores the heteroscedasticity and volatility clustering often affecting financial time series. The proposed methodology is applied to study the reactions of CDS quotes to reviews for downgrading and effective downgradings announced by the three major credit rating agencies (Fitch Ratings, Moody’s, Standard and Poor’s), in order to examine if and to what extent CDS market anticipates announcements related with a company’s creditworthiness. The analysis, focusing mainly on volatility, is performed on two periods, 2004–2006 and 2007–2009, in order to verify whether a change in the signaling power of CDS quotes can be ascribed to recent financial turmoils.

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Notes

  1. These data are from the Bank for International Settlements (BIS 2010)—Semiannual OTC derivatives statistics at end-December 2010.

  2. According to Mayordomo et al. (2010) the CMA database quotes lead the price discovery process in comparison with quotes provided by other databases.

  3. Because of the low number of positive events in the data set (see Table 1), the analysis is carried out only on negative rating events.

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Correspondence to Rosella Castellano.

Appendix

Appendix

The posterior distribution of all the parameters, required for Bayesian inference and given in Sect. 4.3, is simulated via an MCMC algorithm. At each sweep of the algorithm, the following steps are performed:

  • Updating \(\varvec{\Uplambda}.\) The i-th row of \(\varvec{\Uplambda}\) is sampled from \(D(\delta_{i1}+n_{i1}, \ldots, \delta_{ik}+n_{ik}),\) where \(n_{ij}=\sum\nolimits_{t=t_0}^{T-1}I \left(s_t=i,s_{t+1}=j \right)\) is the number of transitions from regime i to regime j.

  • Updating s. The standard solution would be to sample \(s_{t_{0}},\ldots ,s_{T}\) one at a time from t = t 0 to t = T, drawing values from their full conditional distribution \(p(s_{t}=i|\cdots )\propto \lambda_{s_{t-1}i}\phi (y_{t};\mu _{i},\sigma_{i}^{2})\lambda_{is_{t+1}}\) where ‘\(\cdots \)’ denotes ‘all other variables’. For a faster mixing algorithm, we instead sample s from \(p(\user2{s}|\user2{y},\varvec{\Uplambda})\) through a stochastic version of the forward–backward recursion. The forward recursion produces matrices \(\user2{P}_{t_{0}+1}, \user2{P}_{t_{0}+2},\ldots ,\user2{P}_{T},\) where \(\user2{P}_{t}=(p_{tij})\) and \(p_{tij}=p(s_{t-1}=i,s_{t}=j|y_{t_{0}},\ldots ,y_{t},\varvec{\Uplambda}).\) In words, P t is the joint distribution of (s t−1 = i,s t  = j) given parameters and observed data up to time t. P t is computed from P t−1 as:

    $$ \begin{aligned} p_{tij} &\propto p(s_{t-1}=i,s_{t}=j,y_{t}|y_{t_{0}},\ldots ,y_{t-1}, \varvec{\Uplambda})\\ &=p(s_{t-1}=i|y_{t_{0}},\ldots ,y_{t-1},\varvec{\Uplambda})\lambda _{ij}\phi (y_{t};\mu_{j},\sigma_{j}^{2}) \end{aligned} $$

    with proportionality reconciled by ∑ i j p tij  = 1, where

    $$ p(s_{t-1}=i|y_{t_{0}},\ldots ,y_{t-1},\varvec{\Uplambda} )=\sum_{j}p_{t-1,i,j} $$

    can be computed once P t−1 is known. The recursion starts computing \(p(s_{t_{0}}=i|y_{t_{0}},\varvec{\Uplambda})\propto \phi (y_{t_{0}};\mu_{i},\sigma_{i}^{2})\pi_{i}\) and thus \(\user2{P}_{t_{0}+1}.\) The stochastic backward recursion begins by drawing s T from \(p(s_{T}|\user2{y},\varvec{\Uplambda}),\) then recursively drawing s t from the distribution proportional to column s t+1 of P t+1. In this way, the stochastic backward recursion samples from \(p(\user2{s}|\user2{y},\varvec{\Uplambda}),\) factorizing this as

    $$ p(\user2{s}|\user2{y},\varvec{\Uplambda} )=p(s_{T}|\user2{y},\varvec{\Uplambda} )\prod_{t=t_{0}}^{T-1}p(s_{T-t}|s_{T},\ldots ,s_{T-t+1},\user2{y}, \varvec{\Uplambda}) $$

    where

    $$ \begin{aligned} p(s_{T-t}=i|s_{T},\ldots ,s_{T-t+1},\user2{y}, \varvec{\Uplambda}) &=p(s_{T-t}=i|s_{T-t+1},y_{t_{0}},\ldots ,y_{T-t+1}, \varvec{\Uplambda})\\ &\propto p_{T-t+1,i,s_{T-t+1}}. \end{aligned} $$
  • Updating \({\mu}.\) Letting n i being the number of observations currently allocated in regime i, the μ i can be updated by drawing them independently from \({\mu_i|\cdots \sim {\mathcal{N}}\left(\frac{\kappa\sum_{t:s_t=i}y_t + \xi}{1+\kappa n_i},\frac{\sigma_i^{2}\kappa}{1+\kappa n_i}\right)}\).

  • Updating \({\kappa}.\) We sample κ−1 from \({\kappa^{-1}|\cdots \sim {\mathcal{G}}\left(q+\frac{k}{2}, r+\frac{1}{2}\sum_{i=1}^k\frac{(\mu_i-\xi)^2}{\sigma_i^{2}}\right)}\).

  • Updating \({\sigma}.\) The σ i can be drawn independently from an \({{\mathcal{IG}}}\) distribution, i.e.

    $${\sigma _{i}^{-2}|\cdots \sim {\mathcal{G}}\left( \eta +\frac{1}{2}(n_{i}+1),\zeta +\frac{1}{2}\sum_{t:s_{t}=i}(y_{t}-\mu _{i})^{2}+\frac{1}{2\kappa }(\mu_{i}-\xi )^{2}\right)}.$$
  • Updating \({\zeta}.\) We sample \(\zeta \) from \({\zeta |\cdots \sim {\mathcal{G}}( f+k\eta ,h+\sum_{i=1}^{k}\sigma _{i}^{-2})}\).

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Castellano, R., Scaccia, L. CDS and rating announcements: changing signaling during the crisis?. Rev Manag Sci 6, 239–264 (2012). https://doi.org/10.1007/s11846-012-0086-9

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