Andrew Kasapi, senior on-line credit derivatives salesperson at credittrade Ltd., examines two common credit default swap applications—and shows how they can help your credit portfolio.

By now, just about everyone in the derivatives business knows that default swaps are the most common credit derivative instruments around. But how, exactly, can you use them in your credit portfolio?

The two simplest—and most beneficial—applications of default swaps are to create synthetic assets and to hedge cash assets. I'll go through how to do both.

For unleveraged investors, the generic synthetic asset strategy is to write default protection, post the required margin and invest the remaining principal in a near-money-market equivalent asset. Triple-A-rated floating-rate credit-card asset-backed securities are usually the cheapest type of asset for creating synthetic assets.

Banks may want to buy protection on the underlying credit, rather than sell the loan and risk affecting a Banking relationship.

These assets have negligible default risk because of early amortization features and credit enhancement achieved through subordination (12 percent to 15 percent) and excess servicing (3 percent to 6 percent). In addition, the potential loss of premium associated with early amortization events is mitigated by the floating-rate structure of the instruments. The combination of a floater and a default swap equates to a synthetic floating-rate note.

Investors are motivated to use default swaps to create synthetic assets for two reasons. First, relative value. There are times when a synthetic asset is cheaper than the cash-market equivalent. This is especially true when the implied repo rate in the default swap is trading at Libor. As a result, an investor can monetize the repo premium implied in the default swap, without having to finance the trade. Meanwhile, since out-of-favor or volatile credits tend to trade at higher repo premiums, investors can use default swaps to take views relative to the forward credit spreads implied by the default swap market.

A second motivation to use credit default swaps is that the instruments enable investors to tap into a market that's bigger than that of tradable securities. A desired credit exposure that is not available in the cash market can be synthetically created via a default swap. Given the historically low levels of interest rates and the flatness of the yield curve, a disproportionate share of new-issue volume has been both fixed and dated. As a result, the supply of corporate floaters and short-dated fixed-rate bonds has been concentrated in a handful of credits—generally in the financial services.

The number of credits available in the default swap market, by contrast, is far larger, since the exposures financial institutions need to transfer are broader. Banks, for example, may want to hedge a revolving line of credit with an industrial credit by buying protection on the underlying credit, rather than sell the loan and risk affecting a banking relationship. In addition, I anticipate that a large percent of the commercial paper backstop market will be securitized via default swaps—providing another source for synthetic assets.

In Table 1, I compare the economics of synthetic floaters to asset swaps. As shown, the synthetics trade much cheaper. For example, the one-year Anheuser Busch synthetic floater is trading at L+16, or 17 basis points above its asset swap level. For fixed-rate synthetic assets, I recommend investing principal proceeds in the triple-A-rated asset-backed securities of name-brand servicers or agency benchmarks (which fund as well as L-50 in the repo market). Investors can also receive on an interest rate swap or buy eurodollar futures.

Investors may view selling default protection as carrying more risk than investing in the comparable cash assets because of the counterparty risk of the swap. For a protection seller, the risk introduced by a highly rated counterparty is negligible. If the counterparty defaults, the maximum loss to the seller would be the premium, if any, on the swap. Rating agencies have been asked to rate only a handful of default swaps, mainly because default swaps are off-balance-sheet. Moody's approach is similar to that used for credit-linked notes—an expected-loss approach. For a swap, the expected loss is the sum of the expected loss on the reference credit plus the expected loss on the swap—in other words, it's the product of the probability of default and the mark-to-market on the swap. This figure is quite close to zero, since default rates for single-A-rated or better counterparties have run at less than 0.1 percent for the past several years. Hence, the rating of the reference credit is most likely the credit rating of the default swap.

Table 1: Using Default Swaps to Create Synthetic Floaters

Credit	Rating	Term	Protection	AAA-rated ABS FRN	Synthetic Floater	Asset Swap	Pickup
Anheuser Butch	A1/A	1-yr	8	L+8	L+16	L-1	17
May Dept.Store	A2/A	3-yr	21	L+12	L+32	L+25	9
Key Corp	A1/A-	3-yr	18	L+12	L+30	L+25	5

Table 2: Example of Hedge of Hilton Exposure Versus Index

Corporate Spreads, bps	Def. Swap Index (DV01 5.9)		Hilton 7.7 7/02		(DV01 3.4)
	Premium	(T+Spd)	(L+Spd)	(T+Spd)	(L+Spd)
September 15,1997	55	90	60	57	18
August 28, 1996	120	170	100	100	25
Spread Change	65	80	40	43	7
Price Effect, $ Chg due to Spd Duration	$2.21	-$2.72	-$1.36	-$2.55	-$0.42
Chg due to I-rate Duration	$0.00	$3.14	$0.00	$4.03	$0.00
Total Price Change	$2.21	$0.43	-$1.36	$1.46	-50.42

Hedger is buying protection of Hilton (55 bps is offered side quote and 120 is bid side quote).

Table 3: Hedged and Unhedged Portfolios , 10% Hilton, 90% "Market”

Spreads, bps	Unhedged (T+Spd)	Portfolio (L+Spd)	Hedged (T+Spd)	Portfolio (L+Spd)
September 15,1997	60	22	58	20
August 28, 1996	107	33	101	27
Spread Change	47	10	44	7
Price Effect, $ Chg due to Spd Duration	-$2.57	-$0.51	-$2.35	-$0.29
Chg due to I-rate Duration	$3.94	$0.00	>$3.94	$0.00
Total Price Change	$1.37	-$0.51	$1.59	-$0.29

Hedging applications

One of the most important applications of default swaps is hedging. All hedges incur basis risk; the basis risk in a default swap stems from the volatility in the implied repo premium. Since this premium will be more volatile for low-rated and distressed credits, these types of credits will be subject to more basis risk than their investment-grade counterparts. As a rule, the cheapest time to implement a hedge is when the market is not concerned about the risk.

One way to illustrate the effectiveness of default swaps in hedging is to assess how a hedge performed in the past. Consider a hypothetical hedge employed by a money manager benchmarked to the Merrill Lynch Corporate Aggregate, who held 10 percent of the portfolio in Hilton Hotels (Baa1/BBB). In September 1997, this $500 million portfolio had $50 million in Hilton five-year bonds, which were originally purchased at a discount and now have a four-point gain. The remaining 90 percent of the portfolio matches the index in terms of duration and credit quality. Note that this hedge can be viewed generically. One way to reduce a portfolio's exposure to the REIT market, for instance, would be to buy default protection on the most representative credit.

The exposure of the portfolio can be brought back to index levels with either an outright sale of the bonds or a hedge using a default swap. There are three reasons why the portfolio manager might opt to hedge rather than sell: because of adverse tax events (four points of capital gain position), because the cost of hedging is relatively inexpensive (basis could work in favor of hedge), or because of the high transaction cost resulting from low liquidity in the cash market (credit is out-of-favor).

Table 2 represents the components of the hedge—the swap, the cash bond and the benchmark. In September 1997, five-year default protection on Hilton cost 55 basis points. Since the cash-bond asset swapped to L+60, the implied repo rate was L+5. Hence, the bond was cheap to short. Over the course of the year, the fixed-rate spread widened to T+170 basis points and the premium on the swap rose to 120 basis points. The implied repo premium on the swap shifted dramatically. Since the implied repo rate changed to L-25, the hedge netted an additional 30 basis points gain, simply because of the shift in basis.

Index spreads are also shown in Table 2. Fixed-rate spreads widened 43 basis points over this period, but since interest rates fell by more than that amount, the portfolio had a modest gain of $1.48 per $100 of exposure.

Table 3 compares the unhedged portfolio to a portfolio hedged with a default swap. In the unhedged portfolio, the Hilton exposure represents $50 million, or 10 percent of the total portfolio value. Spreads widen by 47 basis points in this portfolio, compared with 43 basis points in the index. In the hedged portfolio, $50 million of protection is purchased, thereby leaving the portfolio flat the Hilton exposure.

The loss resulting from spread duration risk on the cash position is more than fully offset by the change in the premium on the default swap. As a result, the hedge outperforms the unhedged exposure by almost a quarter of a point ($1.59=$1.37). Note that the hedged portfolio also outperforms the 100 percent index-matched portfolio ($1.59 vs. $1.48). The reason: the index is longer, and consequently suffered more from spread duration risk.

Tax implications

Default swaps are an important tax management tool. In the Hilton example, I assumed the bond position being hedged had a four-point premium. If the bond were liquidated, the gain would be subject to capital gains tax for the investor. Since the bond's price experienced a slight appreciation ($0.43), the investor may want to leave the hedge on. Had the bonds been sold in September, the tax event would have equated to $1.40 per $100.

For the $50 million exposure, the tax penalty would equate to a rather startling $700,000 cash outlay (compared with the $550,000 difference between the unhedged portfolio and the index). For this reason, it may be prudent to use a default swap to hedge even when it is trading at a fairly high repo premium.

This example, while an oversimplification of a tax strategy, illustrates the general role of default swaps in tax management.

Arbitrage opportunities

At times, default swaps pricing is sufficiently inefficient to result in profitable arbitrage. Credit default swaps can be used to arbitrage mispricing in the cash and financing markets. Several types of arbitrages can be structured on the assumption that the swap market is forward-looking.

In default swaps, there are two basic market-neutral strategies: 1. buy protection (short), buy the cash bond (long) and fund with repo; and 2. sell protection (long), sell the cash bond (short) and borrow the bond at the repo rate.

The conventional wisdom is to sell protection when implied repo premiums are high and to buy protection when implied repo premiums are low.

So are credit default swaps to this decade what their interest rate counterparts were to the last? While the market is too new to answer this question completely, swaps share many parallels with interest rate swaps. They're important financial instruments because they allow credit market participants to manage credit exposures in new ways, they represent a needed complement to both the cash and financing markets for credit-sensitive instruments, and they can reveal fascinating market information about expected credit risk.

This column is adapted from Mastering Credit Derivatives: A Step-by-Step Guide to Credit Derivatives and Their Application by Andrew Kasabi, © Pearson Eduation Ltd., 1999.

Guillaume Blacher, senior managing director at Reech Capital PLC, describes some of the methodologies used by banks for hedging the volatility risk of complex exotic structures.

All derivative players will agree that books of vanilla options—whether they are options on foreign exchange or a fixed income swaptions, or whatever else—have to be marked consistently with their market price if a realistic profit and loss is to be computed. Failing to do so can lead (and has led) to dramatic hidden losses when the general level of implied volatility changes. Also, in many markets, such as equity options, out-of-the-money puts tend to be more expensive than out-of-the-money calls, and any change in the intensity of this effect (skew becoming more or less steep) will surely have a great impact on a vanilla portfolio. Therefore, each particular European option is usually marked and risk-managed at its own market-implied volatility—that is, the implied volatility quoted in the market for its strike and maturity.

Applying these mark-to-market concepts to exotic options is a much trickier exercise. Since many exotic options involve not only a strike and maturity, but also path-dependent trigger levels at which options can appear or disappear, it is not always intuitively obvious what mark-to-market implied volatility to use for P&L and hedging purposes. In cases of extreme skew, this can be particularly difficult.

Let us take a brief look at knock-out barrier options to explain why.

Knock-out options have a final payoff similar to European options (whether puts or calls) but they can disappear at any time if the price of the underlying security trades above (or below) a certain level. If the knock-out level is set in-the-money (that is, above the strike for a call or below the strike for a put), the option will be called an in-the-money barrier or reverse knock-out. Otherwise it will be called an out-of-the-money barrier or regular knock-out.

Knock-out options can be much cheaper than the corresponding European options, which is enough to make them quite popular. A bullish investor, for example, looking at a vanilla product, might face a cost of 5.6 percent of notional for an at-the-money call option maturing in six months (volatility 20 percent). But if he does not believe there will be much downward movement in the underlying asset over the period, and if he wants to reduce his up-front premium expense, he might be willing to buy a down-and-out knock-out call with a barrier at 95 percent of the current price. This will only cost him only 3.7 percent, and his profile will look as shown in Figure 1.

Figure 1

Conversely, a bullish investor that believes a 25 percent return is the maximum possible rise for the underlying asset over the six-month period might be ready to buy an up-and-out reverse knock-out call that disappears at 125. This would cost him only 3 percent of the notional and his profile will look as shown in Figure 2.

Figure 2

As for European options, closed-form solutions can be derived for both of these barrier options in a Black-Scholes framework with a constant volatility. The problem becomes, What volatility should we use for pricing and mark-to-market when a skew exists on the market? Should we use the implied volatility at the strike (20 percent) or the implied volatility at the barrier, which might be much lower? The reverse knock-out option price will vary greatly depending on the volatility number that we choose, as shown in Figure 3.

Figure 3

This graph indicates, in fact, even more things to worry about: we notice that the Black-Scholes price cannot go above 3.5 percent in this case. What if the price being traded in the market was actually higher than this maximum? That would mean that none of the possible volatility choices can solve for the traded market price within the Black-Scholes assumptions. To solve this paradox, we need to investigate the hedging strategy used by the provider of the barrier.

Delta hedging of reverse knock-outs

The first hedging strategy used by the seller of the reverse knock-out call will be to invest in the underlying asset and continuously readjust that position according to the delta of the option. This will protect the hedger against directional moves of the asset price. This hedge still leaves him with gamma risk, however—a residual risk linked to the amplitude of spot moves, whose impact on his P&L depends on the convexity of the option. When the option profile is convex, he will be hurt by spot moves being higher than those given by his volatility assumption. This could happen at any level when a trader is short a European option and around the strike when he is short a barrier option. When the option profile is concave, which is the case around the barrier in our example, the trader will be hurt by asset price moves being lower than anticipated.

The following two scenarios explain the consequences of these concepts and help us understand the problem of pricing, hedging, and marking-to-market exotic options under a Black-Scholes regime. We assume that a skew exists whereby vanilla options struck at or near the barrier are trading at 15 percent rather than the 20 percent implied volatility of at-the-money options.

First scenario: The trader chooses to price at the strike volatility (20 percent). If the spot ends up around the barrier and its volatility is lower than 20 percent (as anticipated by the market in that implied volatility at the barrier is lower), he will lose money.

Second scenario: The trader chooses to price at the barrier volatility (15 percent). If the spot ends up around the strike and its volatility is 20 percent (as anticipated by the market), he will lose money.

Whatever his choice, he will be dependent on the underlying directional moves, which is to say that his pricing and delta hedge are wrong and incompatible with the market expectations. A better model is needed.

The "smile” model

While Black-Scholes assumes volatility has to be constant, the simplest extension of Black-Scholes that is compatible with market prices of European options and market expectation of volatility at various levels of the underlying is a "smile” model. This model assumes that local volatility is a function of current level and possibly time. In one form or another, it has been implemented by many banks since the mid-1990s and is a major improvement for mark-to-market pricing and risk management. Also, for our up-and-out reverse knock-out option, this model will be able to incorporate different volatilities around the strike and the barrier: a large volatility around the strike (where the option tends to be convex) will increase the price more than Black-Scholes. A lesser volatility around the barrier (where the option tends to be concave) will also increase the price. The compounding of those two effects often leads to a price higher than any Black-Scholes price.

Vega hedging

We have seen that properly taking into account the negative volatility skew can result in a higher price to the reverse knock-out call than using the constant at-the-money volatility. Another knock-out case could be built with a symmetrical profile with respect to the at-the-money option (100 percent). Let's assume we have a three-month option that is a reverse knock-out put struck at 100 percent with a barrier at 80 percent. Let's further assume that the market smile is as follows:

• 20 percent out-of-the-money vanilla puts are priced at 25 percent implied volatility;
• at-the-money vanilla options are priced at 20 percent implied volatility;
• 20 percent out-of-the-money vanilla calls are priced at 17 percent implied volatility.

This time, high volatilities for low spots will affect the concave zone, hence lowering the price, while low volatilities for high spots will affect the convex zone, also lowering the price. Overall the price will go down, as shown in Figure 4.

Figure 4

The reverse knock-out put is worth $5 when priced off the at-the-money volatility (20 percent in our simulation) while it is worth just above $4 when priced with the whole skew information. This leaves the trader selling such an option in a difficult position. Does he really want to sell such an option at a lower price? What if the market skew disappears? This would create an instant loss of $1 in the marked-to-market value of his short position and would lead him to think not marking to the smile was a better strategy! What, then, is the proper approach?

The answer to these questions is quite easy, in fact: it only makes sense to price consistently with European option volatility levels if one is going to hedge the exotic with European options. Doing so will ensure minimal sensitivity to moves of the implied volatility surface (vega sensitivity) and ensure that the trader will not only keep any up-front margin on a deal from a mark-to-market perspective but will also get compensated if the skew disappears.

In the case of the barrier options discussed above, the objective will be to build the best vega hedging portfolio of vanilla options, as may be adjusted over time, computed by performing a sensitivity analysis of the barrier option price to the implied volatilities of each vanilla option available in the market. The hedging portfolio will combine Europeans with the same strike as the barrier option with European options struck at the barrier, with a combination of maturities, as summarized in Figure 5 (reverse knock-out call case).

Figure 5

Final comments

Three important properties of this strategy will impact risk management of barrier options in real life:

Each European option is marked and risk-managed at its own market-implied volatility—that is, the implied volatility quoted in the market for its strike and maturity.

1. This hedge is unfortunately not static and will vary as conditions such as the underlying asset price and volatility surface change. There will often be a systematic rebalancing cost associated with the strategy because of convexity in volatility, and hence the need for a stochastic volatility model for even more accurate pricing.
2. Trading several European options for each barrier option will certainly have a tendency for high transaction costs over time. Therefore, vega hedging has to be performed at the portfolio level in order to benefit from any cancellation of risk between the exotics contained in a market-maker's book.
3. We have only described hedging the proper volatility pricing and hedging of an exotic option. It turns out, of course, that with knock-out barriers, when spot approaches the barrier level, gamma becomes the main source of risk. At the extreme—on an expiration day, for example—this risk will be unhedgeable. In other instances in which an option still has a period of time to run, other hedging techniques, which are beyond the scope of this article, have to be used as well.

Guillaume Blacher can be reached at guillaume_blacher@reech.com.