Let's discuss how MTM of CDS gets calculated. CDS are traded products and booked into trading books, except some exceptions, so these products needs to be marked to fair value daily.
At the inception of CDS, both leg of CDS have equal value but this get change as premium level moves for reference entity. These changes in premium reflects changes in credit quality of reference entity and general market dynamics.These changes in premium cause CDS to have either a positive or negative net present value. For a protection buyer, if the market premium moves wider than the contract premium, he will experience a MTM gain because he bought the protection cheaper than currently available in the market. Vice versa if market premiums tighten. Obviously the protection seller experiences the opposite MTM results.
Calculating a CDS MTM is the same as calculating the cost of entering into an offsetting transaction. Suppose an investor bought 5-year protection at 100bp per annum, and 1 year later the protection widened to 120bp. The investor would then have a MTM gain. To calculate this MTM amount, we can assume a hypothetical offsetting trade where the investor sells protection at 120bp for 4 years, thereby hedging his position. Assume also that the offsetting trade matches the original one perfectly in terms of contract terms, including the same payment and maturity dates, except for the contract premium. This will leave a residual cash flow of 20bp per annum (5bp per quarter) for 4 years in favour of the investor, effectively a 4-year annuity. The present value of this annuity is the MTM amount.
At the inception of CDS, both leg of CDS have equal value but this get change as premium level moves for reference entity. These changes in premium reflects changes in credit quality of reference entity and general market dynamics.These changes in premium cause CDS to have either a positive or negative net present value. For a protection buyer, if the market premium moves wider than the contract premium, he will experience a MTM gain because he bought the protection cheaper than currently available in the market. Vice versa if market premiums tighten. Obviously the protection seller experiences the opposite MTM results.
Calculating a CDS MTM is the same as calculating the cost of entering into an offsetting transaction. Suppose an investor bought 5-year protection at 100bp per annum, and 1 year later the protection widened to 120bp. The investor would then have a MTM gain. To calculate this MTM amount, we can assume a hypothetical offsetting trade where the investor sells protection at 120bp for 4 years, thereby hedging his position. Assume also that the offsetting trade matches the original one perfectly in terms of contract terms, including the same payment and maturity dates, except for the contract premium. This will leave a residual cash flow of 20bp per annum (5bp per quarter) for 4 years in favour of the investor, effectively a 4-year annuity. The present value of this annuity is the MTM amount.
However, we need to bear in mind that these cash flows can cease, since the investor will
receive the 5bp per quarter only until the earlier of a credit event and contract maturity. Upon
the occurrence of a credit event, Credit Event Notices will be served and premium payments will then cease on both transactions, wiping out future annuity payments.
Valuing this annuity payment therefore involves more than just discounting it using risk
free rates. It also involves weighting the annuity with the probabilities of receiving these
quarterly payments, i.e., the probabilities of no credit events occurring before each quarterly payment date. These are the survival probabilities that were introduced in the previous chapter. So, the MTM of a CDS is the present value of an annuity representing the difference between the contract premium and the current market premium, with the annuity cash
flows weighted by the survival probabilities.
MTM = (change in spreads)*(number of periods)*(survival probability)*(discount factor)
Risky PV01- Risky PV01 being the sum of the discount factors weighted by their corresponding survival probabilities, i.e., the sum of the risky discount factors. This risky
PV01 measures the present value of 1bp risky annuity received or paid until the earlier
of a credit event or the maturity of the CDS. The CDS MTM is therefore the annuity multiplied by the PV01.
MTM = Annuity * Risky PV01
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