Modern Derivatives Pricing and Credit Exposure Analysis by Roland Lichters Roland Stamm Donal Gallagher

Author:Roland Lichters, Roland Stamm, Donal Gallagher
Language: eng
Format: epub
Publisher: Palgrave Macmillan

Figure 15.15 Standard deviation of the distribution of fair CDS spread (ln K(t)) as a function of model σ in the BK model for flat hazard rate curves at 50, 150 and 500 bp flat, respectively. Mean reversion speed α = 0.01. The CDS is forward starting in six months and has a five-year term

Calibration and propagation

The BK model calibration to the term structure of CDS fixes the shift function ϕ(t). This requires the calculation of model implied survival probabilities S(0,T) = numerically. It seems common to use trinomial trees for this purpose, refer for example to [33] for the tree construction procedure. The remaining parameters (α and σ) are then determined by calibrating to CDS options, though we have also seen α fixed (not calibrated, but exogenous). With time-dependent σ(t) the model allows calibration to a term structure of options with varying expiry dates. However, the sparseness of market quoted index CDS options (short expiries less than one year only, if at all) may justify using the constant σ version of the model, calibrated to a single ATM CDS option to capture the level of volatility.

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