In order to illustrate the value of the delivery option, all we have to do is walk through a few graphs. Prior to its default, Delphi had four notes outstanding, with maturities from one to twenty-four years. Delphi is an excellent subject for our study of the delivery option because of the way its debt is spread along the curve. It had issues due in 2006, 2009, 2013, and 2029, which is somewhat unusual in the corporate world. Typically, there is less of a spread between the shortest- and longest-maturity debt for most companies except the Agencies. Companies rarely issue 30-year debt, preferring to focus on the ten-year point. Figure 7.1 illustrates the prices for each of the four issues from October 2004 through the default date a year later. This may be the most important chart a credit derivatives trader ever sees. In keeping with our earlier work on a proof by contradiction, we first imagine a world where the buyers of protection have no choice about what issue they must deliver in the event of default.

Suppose that in October 2001 traders who bought protection on Delphi paid a hundred basis points. They did not own any of the underlying notes. The standard ISDA language grants buyers of protection the right to deliver a note with a maturity at least as long as the contract. However, this particular contract specified that delivery must be made with a single note if there were a credit event: DPH 6.55 percent 6/15/06. This would have been a 5-year note in 2001, matching the maturity of the default swap. Going into the end of 2004, things were looking up for Delphi, whose short-term debt was clearly trading at a yield less than 6.55 percent, given the 105 handle on the note price. Our default swap buyers shouldn’t have been very concerned about having specified the underlying note that they had to make delivery with, because the prices of all of four outstanding issues were about the same, or at least within 5 or 10 points of each other. If a 10-point spread seems enormous to a bond trader, it’s nothing compared to what is in store for our protection buyers.

Between the end of 2004 and the start of 2005, Delphi must have still been in fine shape, or at least there was little public knowledge of its troubles, because there was little change in the market for its debt. However, there was a gradual slide in the prices of all of the deliverable issues, although it was quite modest and certainly within the bounds of normal price action. Perhaps it was possible to read more into this slide in prices than met the eye, but at the end of the first quarter of 2005, news suddenly hit that all was not well at the company. Yields moved higher and the prices of the longer-issued debt plummeted because of the higher duration of those issues. However, not much happened to the 6.55% 6/15/06. Its price stayed around par even after word came that Chapter 11 might be an option. Our credit default swap buyers must have been sweating bullets at this time, because they were in an awful situation. According to the contract, they would have to buy the 6.55 percent note in the event of default in order to receive their par payment from the protection seller. However, the 6.55 percent note was still trading around par, even though a default seemed increasingly likely.

The Delphi bankruptcy was official on October 8, although there were certainly strong indications before that that the firm was in financial distress. However, the price of the 6.55 percent note didn’t begin to drop until late August, when it became apparent that Chapter 11 was not simply a possibility but an inevitability.

This price action illustrates a broader point about the behavior of short-maturity bonds in a default situation. Traders seem to be making bets about the timing of default, and if it looks as if a short-dated bond may mature before a bankruptcy filing, it may be immune from the sudden price drops suffered by the longer issues, which is what happened with some of the notes from Delphi. How do you know what the timing of a bankruptcy might be? It is obvious that an outside observer always has less information than a company director, and that information coming from companies is routinely sanitized to omit details that might provide an unfavorable impression of the firm. The general rule of disclosure seems to be: tell as much of the truth as you need to, but don’t go overboard. What may not be as obvious is that even the conditions described in corporate financial materials may have changed substantially by the time that data is actually made public. It can take weeks or months to compile quarterly earnings, and by the time they are released they may lag more than three months behind the activities of the business itself. It is this lag, rather than the good or bad news from a company, that causes panics and noncontinuous price jumps in the securities markets. The point being: By the time any unfavorable news leaks out of a company, the truth is likely worse than the firm is letting on, and it is already too late to do much about it. The moral of the story is directed at the traders who owned the 6.55 percent Delphi (DPH) notes: timing defaults is a fool’s errand. These notes were due in June 2006, and Figure 7.1 illustrates that as late as August 2005, traders were hoping that they would mature and be paid off at par before the Chapter 11 filing.

A world where the delivery option does not exist can still be a complex one, as the price behavior of the 6.55 percent note indicates. In this case, conventional wisdom was that Delphi’s finances wouldn’t unravel as quickly as they did, and even when some notes were trading at seventy cents on the dollar, the shortest-dated issue held on at par. Delivery options seem tame by comparison with this game of financial chicken, in which traders looked default in the face but still bet that their note would mature before the default wiped out half of their holdings. Even the presence of a kamikaze trader in the issue wouldn’t matter if the buyers of protection had the choice of delivering whichever note they pleased. The kamikaze is going to bid up the shortest-dated note if there is any chance of it paying off at par, whereas the traditional default swap buyer simply wants the instrument to represent the loss of value of the underlying note. Granting protection buyers the right to choose which issue is delivered into the contract does add some complication to the instrument, but it solves more problems than it creates.

We now consider a more complicated world where the delivery option does exist and the buyers of protection are rescued from having to deliver the 6.55 percent note that hung around a par price for so long. Although the buyers of protection are not told which note to deliver, a savvy trader would choose the issue with the lowest dollar price, and in Figure 7.1 this would mean finding a note with the lowest line along the y-axis at any point in time. If the buyer of protection is going to receive par no matter what note is delivered, it makes sense to spend as little as possible to get that payment. Although the prices of all the issues were approximately the same prior to the onslaught of problems in 2005, the original 30-year issue had a price that was just below the others at this point, with a price in the high 90s. Obviously, as time wore on, the yields of all of the notes were going to increase, but the high duration of the 7.125 percent note caused its price to drop precipitously. Anyone wondering whether or not the delivery option has value need only look at the performance of the 6.55 percent and 7.125 percent notes to see the dramatic difference. As illustrated in Figure 7.1, there was, at the most, as much as a 30-point difference in price between the cheapest and richest issues from Delphi.

The conclusions to be drawn from Figure 7.1 appear obvious enough: the prices of all the issues were not the same. But this doesn’t do justice to the data. Follow the price of the 7.125 percent issue from the far left to the far right of the graph, from a period when everything seemed to be going reasonably well for the company to the moment before it filed for Chapter 11. The value of the delivery option is not obvious from the simple observation that the 7.125 percent issue had the lowest price for the entire time, because this is not true. The 7.125 percent note had the lowest price for almost the entire time, but not at the very end of the series, starting at the very end of September. Just a few days before the October 8 filing for Chapter 11, the 7.125 percent issue was bid up so that it no longer had the lowest dollar price in the basket, as is apparent from the solid black line creeping above the gray line. The bid to what was the cheapest issue in the basket speaks to the essence of the delivery option, highlighting the point of the whole system. When buying pressure intensifies and the cheapest issue rises in price, the cheapest issue may change, effectively increasing the supply of notes available at the same price. This is exactly how the delivery option is supposed to work to eliminate the peculiarities of any particular issue. If the cheapest issue rises in price a great deal because of an impending delivery due to default, then the price gap between the cheapest and second-cheapest issues will shrink. The system was originally developed to avoid squeezes in the Treasury market, but here it is apparent that it is helping to avoid squeezes in corporate bonds.

One question needs to be answered: What happens if protection buyers purchase a deliverable note anticipating a default, but the price of that note continues to fall? The question isn’t an academic one, as Figure 7.1 illustrates, since Delphi’s long-dated maturities fell to a price of between 70 and 80 points in March 2005, but remained relatively stable within that range until August of that year. However, after August, the prices of all the notes slid further. If protection buyers had purchased notes at 80 in anticipation of a payout of 100, but the price of the notes continued to drop, what would their return have been? Remember that the default swap had a price of its own, as illustrated by the heavy black line at the bottom of Figure 7.1. The scale is quite compressed on the right-hand y-axis, but it’s clear that the default swap price spiked at the same time that the note prices were falling, first in March and then again in August of 2005. Presuming we can measure the risk of each underlying note and the default swap, it is possible to create a ratio where the price risk of the two sides offset each other. When the protection buyers purchased the notes to make delivery with, they locked in their profit or loss on the trade. If the protection was purchased in a default swap as a hedge in a portfolio that included the cash notes, then none of this mattered, because the default swap price appreciation offset the loss of the note. If protection was purchased by traders who had no ownership of the underlying notes, then the trade worked out quite well, as the traders benefited from the jump in price of the default swap. But the moment the underlying notes were purchased to make delivery, the price action of the two offset each other, and the profit or loss of the trade was fixed. If protection buyers purchased the note at 80, but the price slid to 60, then prior to default they would have been hedged because the default swap was appreciating to cover that 20-point loss. However, at settlement the default swap only entitled the protection sellers to pay par for the notes, so the profit for the people who bought the note at 80 cents on the dollar was 20 points; they would have missed out on another 20 points if they had just waited to unwind the trade by buying the note at a price of 60. Of course, the trade wasn’t being unwound, because it was still necessary to go through delivery, but the profit or loss of the trade was fixed, and the position was essentially on autopilot to collapse by itself if there were a default.

Following the performance of the deliverables basket in a corporate default is difficult, but viewing the same data as a cross section of prices at a single point in time highlights the value of the delivery option. Figure 7.2 illustrates both the prices for notes in the deliverables basket for 10-year Treasury futures as well as the price differences compared to the cheapest in the basket. Viewing the basket in terms of price differences is the most important step to the analysis, because there is nothing we can do about the absolute level of prices or yields; instead, the delivery option is concerned with the right to choose across the basket for the lowest-price issue. In this case the price difference between the cheapest and second-cheapest issues is the incremental price of delivering the second-cheapest issue. It is the structure of the price differences between issues that determines the delivery option, but consider what happens if the cheapest issue is bid up in the market in a squeeze: as the price of the cheapest issue increases, the price gap falls. When the gap is gone, there is no economic difference between delivering the cheapest and second cheapest issue. Effectively, the bid to the cheapest issue has opened up an entirely new supply of bonds with the same economic value. Take any demand function and double the supply, and I guarantee that it will cool the price appreciation. These mechanics play out every day in the Treasury futures market, and basis traders have become expert at analyzing changes to the basket, but what about the Delphi bonds? Can corporate traders be expected to respond to the same incentives that shape the behavior of the futures market, but without the benefit of regular quarterly deliveries? Figure 7.3 holds the answer.

Figure 7.3 illustrates the price differences of the four Delphi bonds we’ve identified in terms of differences in price from the cheapest in the basket. Initially, the longest issue, the 7.125 percent original 30-year maturity, had the lowest price, and it registered a zero price difference with itself. A zero price difference isn’t very illustrative, except when we look at what happened to the relative prices of the issues in the basket over time. On March 1, 2005, the 7.125 percent had the lowest price by a margin on several points, as illustrated by the difference between the cheapest and the second-cheapest issues in the basket. Again on September 30, the 7.125 percent issue had the lowest price, but this time the gap between the cheapest and second-cheapest issues had actually dropped. This drop in relative prices is indicative of the buyers of protection responding to the correct incentives: bidding up the cheapest issue to minimize the loss incurred by the protection seller. If there weren’t some check on the downward spiral of a defaulted issue, the seller of protection could be on the hook for an absurd loss, far in excess of the best guess of the market going into default. The narrowing of price differences between the cheapest and second-cheapest issues isn’t a sign of manipulation, or that cheapest-to-defiver-style contracts manipulate the market, but of the fact that the derivative is closely tied to the value of the cash notes, which is entirely appropriate.

As we mentioned, it is the price action immediately prior to default on October 7 that best illustrates the delivery option. On this day, the 7.125 percent bond was bid up so much that it was no longer the cheapest in the basket. That honor switched to the next-longest issue, the 6.5 percent due in August 2013. The price difference between this issue and the 7.125 percent was now several points in the opposite direction than in the first two time periods illustrated. Consider what happened with this switch. The buyers of protection bid up the original cheapest issue to such an extent that a second issue now had the lowest price. This is an easy example to use in considering the supply implications, because all four issues have a $500 million face value. On October 7, the supply of notes doubled as the two issues crossed paths with the same price. The cheapest-to-deliver framework delivered added supply in order to prevent manipulation of a particular issue. While it is true that the buyers of this note had to give up the original cheapness of the note compared to the second cheapest issue, the structure did put in place a speed bump by letting the buyer choose the 6.5 percent issue with a lower price on October 7. This example highlights the workings of a cheapest-to-deliver-style delivery as well as the tradeoffs that are necessary in contract design.

As with our earlier examples of quantifying the delivery option, we can use market prices to quantify the value of the delivery option in our Delphi example. Figure 7.4 illustrates the same data as Figure 7.1, but this time as a cross section rather than a time series. While we lose the order of the data, we are able to create a performance profile that will be of more use to us in valuing the delivery option. Following along the lines of our first example, where we considered the price and yield of the 5-year note as if we had no choice but to deliver this issue, we chart its performance against the note with the lowest price in the basket, which, up until the last few days prior to default, is the 30-year issue. Obviously there is quite a gap in performance between the two issues. The important question in pricing the delivery option is not simply what the price difference is, but how much it would cost to create a basket of options so that the performance replicates the gap between the two series. Of course, the options market for corporate debt isn’t as well developed as it is for interest rate derivatives, but from here on out we rely on Black-Scholes model prices for the naked options basket—with the caveat that executing these trades in the cash market would likely be more expensive than a model would predict. Black-Scholes, however, provides a useful baseline for the analysis.

Figure 7.5 illustrates the same data as Figure 7.4, except this time we have calculated the return of the cheapest-to-deliver series in terms of differences from the note with a tenor that matched the expiration of the default swap. For practical purposes, we are measuring the difference between the performance of the 6.55 percent June ‘06 against the 7.125 percent May ’29. We let the computer search for strikes that create a replicating basket of five options to match the underperformance of the 7.125 percent compared to the 6.55 percent. There is no particular reason why we chose five, except for convenience. The computer could create a better-fitting portfolio with more strikes, but practically speaking the larger the option portfolio, the more difficult it is to keep track of an execute. We consider only the intrinsic value of the options for fitting purposes, so that we can then use Black-Scholes to give us the prices of those options at any point prior to expiration. The portfolio of naked options in this case would have hedged the Delphi defaults—all puts, remember, because we are moving from a shorter to a longer issue.

The cost of hedging against a delivery option can be quite prohibitive. However, remember that we hedge against a delivery option today for an uncertain future. The chance of default is not 100 percent, and to appropriately value a delivery option, we have to multiply the option value by the probability of default. Earlier we calculated that the chance of default, assuming a 40 percent recovery rate for a premium of 7 basis points, was around 1 percent, which means that the probability-weighted delivery option value in this example is $700 ^* 0.01 = $7, or a present value of even less than $1. As the probability of default increases, so will the probability-weighted value of the delivery option. It took evaluation of all the different pieces of default swap modeling in order to fully appreciate the interaction of the credit option on default as well as the interest rate option on the cheapest issue. As if this weren’t complicated enough, the two options interact with one another!

We mentioned that the probability of default depends on the premium of the default swap: a higher premium implies a higher probability of default. Similarly, the general rule is that the greater the dispersion of maturities for deliverable notes, the greater the value of the delivery option. Careful reflection on the work we have done so far should raise some warning flags, the primary one being that the premium for a default swap includes the value of the embedded delivery option. So how can we use this information to independently arrive at value for each part? The problem is that we have to rely on default swap premiums to generate default probabilities. These default probabilities are necessary to value the probability-weighted delivery option. We can then subtract this value from the default swap premium to distinguish between the credit and interest rate options. An analytical example makes the conundrum concrete. Suppose that we observe a default swap premium of 10 basis points, and using this premium we back out a flat default probability curve of 5 percent each year of the contract. If the delivery option value were worth 50 basis points in premium, we would calculate the probability-weighted value of the delivery option to be 2.5 basis points:

There is no solution to this problem, except to agree on a two-stage estimation process. The first pass will take the default swap premium and back out default probabilities, which we will now consider to be fixed, even though we know they are probably slightly too high because they were derived from a premium that included the price of the delivery option. The next stage is to calculate the value of the delivery option and multiply it by the probability of default to arrive at a default probability-weighted value of the delivery option. The proportion of the default swap premium not allocated to this value is the option-adjusted premium for the default swap. Just as in a single equation with two unknowns, we can’t solve for one of the variables without first fixing the other. There is a way to get around this problem, though it is imperfect at best. Although the vast majority of default swaps make no restrictions on the maturity of the note that is deliverable, it is possible to create contracts where a single deliverable issue is eligible for delivery in the case of default. This second reference point is a way to let the market price the value of the delivery option. If we have one contract that allows for any underlying note to be delivered and one that requires a maturity that matches the expiration of the contract, then we compare the two and observe what the market thinks the value of delivery option should be.

However, this market-based approach is far from perfect. What happens when we take a market where the vast majority of the structures are the same, and we ask for something atypical? Dealers may make a market in the structure, but only at a price. With no means of offsetting customized contracts, dealers sometimes have to warehouse and actively manage the hedges for these types of contracts, which all come at a higher price than if the structure were more typical of the rest of the market. While it is possible to compare the two prices from a dealer, one for a contract with a delivery option and one for a contract without it, we certainly have to take this price difference with a grain of salt, because the economics of the situation demand an upward bias on the premium of a custom contract with no delivery option. Another reason we might take this market price with a grain of salt is the fact that we are simply passing the buck for our responsibility to price the credit and interest rate components of default swaps to a trader who doesn’t necessarily know more about his or her market than anyone else. Old traders from the floor of the Chicago exchanges used to say that they could trade any market, no matter the underlying commodity, as long as there was some kind of volatility. As long as prices moved, if didn’t matter to these traders if the contracts they were buying or selling were based on soybeans or Treasury notes. Some of this spirit lives on today on Wall Street, and market making doesn’t always depend on an intimate knowledge of the underlying product.

In addition to the ad-hoc auction process to determine the value of default swaps in the Delphi default, pairs of dealers have been arranging bilateral agreements known as “lock-ins” to either cancel or settle trades. While some of these trades involve Delphi, the arrangements are part of the broader effort to reduce the backlog of trades in the default swap market, which has grown far in excess of the infrastructure available to handle it. The Delphi default highlighted how far the infrastructure of the market had yet to come. It proved to be a labor-intensive ordeal, leading to an inconsistent mix of solutions. Inconsistency is the antithesis of a derivatives contract, and can only restrain trading activity. The fact that notional volume has grown so fast in the product suggests that its utility is so great that traders are willing to ignore the problems associated with the contract. The CDX consortium is doing exactly the wrong thing with its movement toward auctions and cash settlements, because these destroy the value of the delivery option, unfairly favoring the seller of protection over the buyer. It may not come as a surprise that this solution was proposed by many of the same Wall Street dealers who are leading sellers of protection. Given how new the market is, it is entirely possible that the traders who agreed to break the terms of their contracts and accept the auction price for the Delphi contracts didn’t fully appreciate the value of the delivery option. Delphi won’t be the last company to declare bankruptcy. Traders armed with an understanding of the mechanics from this chapter will be able to make informed decisions about how to handle the next credit event in the default swap market, and perhaps they will avoid the mistakes of their predecessors.