# Credit-Default Swap Index Options

Though credit-default swap index options have been around for a few years, investor interest, liquidity and volumes have increased significantly only this year.

Though credit-default swap index options have been around for a few years, investor interest, liquidity and volumes have increased significantly only this year. This growth is partly attributable to increased liquidity of the underlying CDS index market that has reduced the cost of hedging options and standardization of the CDS index option market through introduction of ISDA documentation. The accounts involved have included real-money managers, hedge funds and proprietary trading desks. In North America, traded CDS index options are on the Dow Jones CDX set of indices: CDX Investment Grade (CDX.NA.IG: comprised of 125 names), CDX High Volatility (CDX.NA.HVOL: 30 names), CDX Crossover (CDX.NA.XO: 35 names), and CDX High-Yield (CDX.NA.HY: 100 names). In Europe, traded CDS index options are on the iTraxx Europe set of indices: iTraxx Europe (125 names), iTraxx HiVol (30 names), and iTraxx Crossover (45 names).

Mechanics

Two types of CDS index options trade: payers and receivers. All CDS index options are European style, i.e. they can only be exercised on the expiry date. A payer option holder has the right but not the obligation to buy protection on the underlying index at the strike spread level on expiry. Similarly, a receiver option holder has the right to sell protection at the strike spread level. At any time, options with expirations on the next two to three CDS market roll dates (December 20, March 20, June 20, September 20, or next business day) are most liquid. Other expirations are also common and options with up to one-year tenor have traded in the market. The underlying index is usually the on-the-run five-year index as of the trade date. Interest in the seven and 10 year tenors of the on-the-run index is steadily increasing.

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.

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.

Note that options on single name CDS treat defaults differently. Unlike index options, single name CDS options knock out in the event of a default.

Pricing

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:

where, d(t) is the discount factor for time t, T is the maturity date of the option, and E[] is the (risk-neutral) expectation operator. The two components of the payoffs are in turn given by:

where,

Current market practice is to calculate the expectation of the first term (payoff from spread level) by using a standard **Black** 1976 model for pricing options on swaps. This is similar to the model used in the interest-rate swaption market. Trader runs will often provide the volatility implied from this model. The expectation of the second term is calculated simply by noting that *E*[I(*T*)] = *p*(*T*), where *p*(*T*) is the probability of default by time T. For each name, we get the default probability by using standard CDS bootstrapping methods on the CDS curve for the name.

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Strategies

A typical strategy portfolio managers have utilized is buying out of the money payer options to protect a long credit portfolio in the event of dramatic credit spread widening. Many portfolio managers prefer this strategy compared to buying the underlying index protection because their maximum downside is limited to the upfront option premium paid. Also, the current implied volatility for out-of-the-money options is fairly close to that for at-the-money options. This suggests that the out-of-the money options are not significantly more expensive--in implied volatility terms relative to at the money options--as is sometimes the case in other option markets.

Another common strategy is writing a payer option to reduce the cost of holding a short position in the underlying index. Investors using this strategy reduce the cost of the index short, but in turn, give up some of the upside from spread widening. The table below illustrates this strategy with a simple example. Trade 1 is an outright short index position on USD 100mm of CDX.IG.7, and Trade 2 is the same position paired with short position in USD 100mm of a 20 March 2007 payer option with 35bp strike. We show the initial and net cash flows of both trades assuming index spreads are at current level (34bp), tighter by 5bp, or wider by 5bp/10bp on 20 March 2007.

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.

Investors have also started using the CDS index options market to express views on CDS index volatility. Recently, implied option volatility has been significantly higher than daily realized volatility of the underlying index. For example, implied volatility calculated from options on the CDX.HVOL index are currently around 35% whereas recent realized volatility for HVOL is closer to 25%. This observation has led to some investors selling straddles--effectively shorting volatility--in the expectation that implied volatility will fall towards the realized volatility levels. With this developing credit volatility market, we have also seen some cross-market traders express relative value views between credit and equity vol.

Concluding Remarks

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 USD250mm notional. As the investor base for this product is growing we expect to see volumes continue to increase rapidly next year.

*This week's Learning Curve was written by**Tahsin Alam**, quantitative credit strategist and**Matthew Simpson**CFA, credit derivatives trader, at Deutsche Bank in New York.*