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- Markit Credit Indices A Primer
CDS index options offer a new risk/reward profile for credit investors. We expect index options to gain in popularity as investors use them for hedging and for expressing specific credit views difficult to express otherwise. Bid/offer spreads in CDS index options have compressed and market liquidity has been very good with typical investment grade trades in excess of USD755mm notional. As the investor base for this product is growing we expect to see volumes continue to increase rapidly next year.
CDS Indices and swaptions are intertwined | IHS Markit
Morini and Brigo addressed the issues above, using a sub-filtration method, where they defined the so called no-Armageddon pricing measure that is equivalent to the risk-neutral probability measure, and consequently, they obtained an arbitrage-free option valuation.
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The payoff of a CDS index option has two components: payoff due to difference in spread level at expiry and strike, and payoff due to any default losses. The price of an option is the discounted expected payoff with expectation taken using a suitable risk-neutral measure. The price for a payer option, for example, is given by:
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You then have to adjust the forward rate that you enter. To do so you must calculate the value of the front end protection (PV of a protection leg to the forward start date) and then amortise this over the life of the index swap by dividing by the forward period index risky PV56.
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Options use physical settlement. An investor who exercises an option becomes either long the credit risk or short the credit risk of the underlying CDS index depending on whether the option is a receiver or a payer respectively.
Markit Credit Indices A Primer
If a default happens among the index constituents prior to option expiry, the buyer of a payer option or seller of a receiver can trigger a credit event on option exercise. Since the buyer of a payer option receives any default losses, it may be profitable to exercise a payer option even if the index spread is below the strike. Thus defaults increase the range over which a payer can be profitably exercised. Similarly, since the buyer of a receiver option has to pay default losses, defaults decrease the range for profitable exercise of a receiver.
The issue with this formula is that the numeraire, the Index Defaultable Present Value per Basis Point , or the forward PV56 , can be zero with a positive probability, and, as a consequence, the swap measure is not equivalent to the risk-neutral probability measure.
You will need to calculate a few extra terms to make these adjustments which are all set out. These will need you to extract the index survival probability curve from index spreads using a standard CDS valuation model.
As we can see, writing a payer option reduces the cost of holding a short credit position in a stable/tightening spread environment, while reducing some of the upside if spreads were to widen. Note, however, that if the option is exercised, the option writer loses the short index position and does not benefit from any future spread widening.