IMPLIED SURVIVAL PROBABILITYCalculating implied survival probabilities from CDS prices follows the same idea, as calculating implied volatility from option price. For options, we have known market price, from which we can numerically solve the corresponding option volatility by using option pricing model. For CDS, we have known market price, from which we can solve the corresponding survival probability by using CDS pricing model. This is exactly the procedure, what this algorithm is doing. However, instead of just calculating one survival probability for a given CDS price, the algorithm is calculating all survival probabilities for a given CDS term structure. The pricing model for CDS is standard model (JP Morgan approach).
Update (9.11.2016) : This presented implementation (using simple JP Morgan CDS model) ignores the effect of premium leg accruals. The resulting bias is relatively insignificant for low CDS levels but becomes material with high CDS levels. The issue has been chewed in the paper published by Lehman Brothers Fixed Income Quantitative Credit Research (Dominic O'Kane, Stuart Turnbull). On chapter 5, there is a discussion concerning premium leg valuation and related accrual effects. There is also a suggestion available for including premium accrual into this CDS pricing model. Thanks for attentive blog visitor for outlining this issue.
FUNCTION INPUT/OUTPUTZero-coupon bond prices, CDS prices and recovery rate assumption are needed as market data input for calculations. VBA function survivalProbability takes market information matrix (curves) and recovery rate assumption value (recovery) as input parameters. Function then returns an array of survival probabilities. Default probabilities can then be calculated from survival probabilities.
Input market information matrix (N x 3) should contain the following data in the following order:
- 1st row vector - maturities in years
- 2nd row vector - zero-coupon bond prices (ex. 0.9825)
- 3rd row vector - CDS prices as basis points (ex. 0.25 % is given as 25)
After giving required input parameters for this function and selecting correct range for function output, remember to press CTRL+SHIFT+ENTER for retrieving result array (N x 1) into worksheet.
The following Excel screenshot presents the calculation of default probabilities for Barclays and HSBC. Market data has been retrieved in early january 2014. VBA function input matrix (curves) has been marked with yellow color. Function output range has been marked with blue color. Default probability (PD) is calculated in column G.
Thanks for reading.