Risk-neutral transition matrix

Use of transition probabilities from credit agencies can be accommodated in some of these models. The formation of the risk-neutral transition matrix from the historical transition matrix is a key step. 

Default can take place randomly over time, and the default probability can be determined using the risk-neutral transition matrix. 

The statistical transition matrix is adjusted by calibrating the expected risky bond values to the market values for risky bonds. The adjusted matrix is referred to as the risk-neutral transition matrix. The risk-neutral transition matrix is key to the pricing of several credit derivatives. 

The JLT model allows the pricing of default swaps, as the risk neutral transition matrix can be used to determine the probability of... 

The Das-Tufano (DT) model is an extension of the JLT model. The model aims to produce the risk-neutral transition matrix in a similar way to the JLT model however, this model uses stochastic recovery rates. The final risk neutral transition matrix should be computed from the observable term structures. The stochastic recovery rates introduce more variability in the spread volatility. Spreads are a function of factors that may not only be dependent on the rating level of the credit as in practice, credit spreads may change even though credit ratings have not changed. Therefore, to some extent, the DT model introduces this additional variability into the risk-neutral transition matrix. 

Various credit derivatives may be priced using this model for example, credit default swaps, total return swaps, and credit spread options. The pricing of these products requires the generation of the appropriate credit dependent cash flows at each node on a lattice of possible outcomes. The fair value may be determined by discounting the probability-weighted cash flows. The probability of the outcomes would be determined by reference to the risk neutral transition matrix. 

In practice, assuming the discrete time case, the transition matrix includes the transition probabilities between the possible states. Therefore, in this model, market prices are used to find the credit spread and convert the matrix of transition probabilities to the time-dependent risk-neutral matrices Qt t+i- The credit spread is given by Equation (8.32) ... 

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