March 1990

COMMODITY FUTURES NVjrch 11,

Covered Call Options: A Proposal to Ease LDC Debt

Steven P. Feinstein and Peter A. Abken

The large debt burden carried by many developing nations not only has hampered these countries' economic development but has also threatened their commercial lenders. Economic austerity measures aimed at

CATTLtiEp»£R. (Liuti HtoM* ) p., lb reducing this debt have severely limited the funds less ca«5 SirtWr P„li Mir < Apr <• MavìUv-t-. Vi' p A frf Mav ? developed countries have available for domestic invest- »VI 0.00 on o v 0 do o 70 ment, further retarding their economic growth. The authors' proposal—that LDCs sell -term, high call options on their chief export commodities—would Aft J«P v,î allow LDCs to generate revenue without renegotiating existing debts or giving up ownership of productive resources.

any less developed countries (LDCs) of debt relief is not a physical commodity but struggling to pay off massive rather a type of financial asset—namely long- Mpossess an untapped, exportable term, high strike price call options on their chief resource for which a demand exists in devel- export commodities. oped nations. Revenue from such a resource The proposal in this article offers interested would not only help to service debts but also parties such as commodity users or speculators further the indebted developing countries' the opportunity to bid on the right to purchase a economic advancement. This potential source certain quantity of a chief export commodity for

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a prespecified price on a given future date. In making these call options available, LDCs would The World Debt Problem—A Review in effect be sel ling commodity price - insurance that pays off if the commodity price Since 1982 the high indebtedness of many rises beyond some high level. For example, a developing nations has placed a severe strain bidder might purchase the right (but not the on both the LDCs and the world banking com- obi igation) to buy Mexican oil at $27 a barrel on a munity. According to the most recent account- given date five years hence, even though the ing, LDCs owe $1.3 trillion to foreign , price of oil at the time of bidding is only $ 17.25. governments, and international agencies.3 Not Should the prevailing market price remain be- only have LDCs struggled to service this debt, low the "strike" level of $27, the owner but exposure to these troubled loans has would simply elect not to carry out the transac- threatened the strength of commercial banks. tion.1 Should oil rise to $30 a barrel by the The roots of the problem can be traced to the agreed-upon date, though, the bid- of commodity prices and interest rates der could purchase the oil at $3 below prevail- over the last two decades. The oil price increases ing prices. Although the LDC must then re- of 1973 and 1979 led to a massive redistribution linquish goods for less than the going rate, of wealth from oil importers to oil exporters, revenue from the earlier option sales would primarily those in the Middle East. These "pet- have ameliorated matters during a period of low rodollars" accumulated in commercial banks prices. The loss of potential profits would come around the world as surplus funds awaiting in- at a time of high prices when the selling country vestment opportunities. Because of their ap- could best afford it. parent excellent potential to develop rapidly, Using call options in meeting debt obliga- Latin American economies were deemed to be tions is not an entirely new idea. Numerous excellent risks. As a result, these coun- articles in academic journals have suggested tries received enormous loans from commer- construction of financial instruments that tie a cial banks. borrower's liabilities to a commodity price, and The loans were predominantly short-term, the recent Mexican restructuring (described with interest rates tied to the London Interbank below) includes such a feature.2 In other plans, Offer Rate (LIBOR).4 By 1980 three-fourths of the however, options have been bundled together debt owed by Latin American countries was set with bonds. By selling options separately, as at variable rates; 40 percent was due for repay- proposed here for the first time, an LDC can ment within one year, and 70 percent within generate substantial revenue without renegoti- three years.5 From 1971 to 1980, LIBOR was on ating all its outstanding debts. average 0.8 percent (80 basis points) less than Such an "unbundled" approach is possible the rate of U.S. wholesale price inflation; de- with this proposal because it calls for selecting a veloping countries were effectively borrowing at strike price high enough to ensure that the very low or even negative real interest rates.6 debtor will face the future obligation only when Later, however, rates on LDC debt surged as the fulfillment of all other obligations is relatively United States tightened monetary policy in an easy. This feature would obviate the need to attempt to control inflation. LIBOR averaged 9.2 gain the endorsement of existing creditors prior percent (920 basis points) above the U.S. infla- to selling the options. Keeping the options tion rate from 1981 to 1982.7 As rates rose, debt separate from debt instruments also affords the service obligations soared. LDC greater flexibility in the management of its The worldwide that accompanied revenue flow and debt. A program of selling higher interest rates further hurt LDCs. Reduced options when commodity prices are low and redeeming them when prices are high can help an LDC smooth revenue across periods of high The authors are economists in the financial section of the and low commodity prices. A further advantage Atlanta Fed's research department. They would like to thank Marco Espinosa, Larry Wall, and Robert Kahn for helpful is that the market for the unbundled option is comments. They gratefully acknowledge research assis- likely to be wider than the market for options tance provided by Karen Hunter and Hermawan Djohari. coupled with debt. The authors accept sole responsibility for any errors.

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demand for their exports and plummeting com- debt. Mexico received concessions on principal modity prices compounded their misfortune. As and interest, along with new loans (Peter Tru- the value of imports began to overwhelm that of ell 1990). exports, current account payment balances of The LDC debt problem, however, is far from the highly indebted countries turned sharply over. No single approach is likely to work across negative.8 By the end of 1982, 34 developing the board, and in mosteases debt reduction will countries were unable to service their debt probably be part of future financial arrange- fully.9 As oil exporters, Mexico and Venezuela ments. Yet developing countries that rely solely were special cases. As oil prices leveled off and on debt reduction may find it difficult to borrow then began to drop, however, these two coun- in the future. Nor is rescheduling old loans and tries also began to have difficulty making pay- securing new loans a satisfactory long-term so- ments on the substantial debt they had ac- lution. Many experts now agree that the prob- cumulated against future oil revenues. lem is one of solvency rather than a lack of The predicament has taken a heavy toll on the liquidity available to the LDCs (Anna J. Schwartz LDCs. In net terms Latin America and the Carib- 1989). In other words, these nations' economic bean exported capital in each of the last eight prospects are sufficiently bleak that markets years; the 1989 net outflow amounted to $24.6 doubt LDCs can make good on their past financial billion (see Barbara Durr 1989). As a result, obligations. Consequently, as long as stretching domestic investment and development have payments out over longer horizons preserves suffered. Growth over the last decade has slowed the net present value of LDCs' liabilities, such a to a crawl, making repayment of the foreign debt tactic will not end the crisis. even more difficult and less likely.10 Moreover, Highly indebted countries must therefore standards of living have declined. Between 1980 search for ways to restore their solvency. Essen- and 1987, per capita consumption in the LDCs tially, in order to pay off their huge debts, they fell nearly 12 percent (see Giancarlo Perasso must raise more revenue. Better economic plan- 1989, 535). If the quality of life for the citizens of ning and measures to stem domestic capital LDCs is to improve, many believe, capital must flight are the sorts of actions that will have last- flow into these countries on net, not in the ing positive effects (A. Schwartz 1989 and Ru- opposite direction. diger Dornbusch 1987). Some policymakers and Lenders have also suffered. In 1982 the sum of analysts advocate debt- swaps as means LDC loans on the books of U.S. banks was over by which LDCs can pay off loans without incur- 180 percent of the capital in those banks (Jeffrey ring new liabilities; however, these transactions Sachs 1989a). Since then, the market value of represent permanent sales of an LDC's produc- LDC loans has fallen sharply below book value. tive resources (such as forests, mines, and fac- For example, by March 1990, Peruvian loans tories) and so cannot provide revenue on a could be sold for only six cents on the dollar, continuing basis. Consequently, such swaps and the market valued Mexican debt at 40 per- serve only as temporary palliatives. Further- cent of face value.11 Consequently, bank earn- more, the manner in which debt-equity swaps ings have suffered, and bank have re- are executed usually results in flected deteriorating loan portfolio values expansion in the LDC, thus fueling inflationary (Sachs 1989a). pressures.12 Nonetheless, considerable progress has been made toward alleviating the crisis. Banks have reduced their LDC loan exposure and increased capital, thereby easing fears of bank insolvency. A New Proposal By 1988, aggregate exposure stood at less than 80 percent of capital (Sachs 1989a). This im- Selling high strike price call options on export provement afforded some breathing room and commodities is one way LDCs could generate made it possible for banks to offer debt relief. revenue without selling their productive resour- Recently, U.S. Treasury Secretary Nicholas ces or renegotiating existing debt. Thus com- Brady's initiative to reduce LDCs' debt burden modity price volatility, which contributed to the helped Mexico restructure its commercial bank debt crises in the first place, could provide a

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partial key to its solution. It is precisely the The is a simple use of options. volatility of LDC export prices that makes high Additional flexibility could be achieved through strike price call options valuable today, just as use of combinations of options, which would, for uncertainty makes various forms of insurance example, keep an LDC from sacrificing all of the more desirable. additional revenue forgone if prices rose above Because a affords the buyer the the strike price. A more elaborate use of options right, but not the obligation, to buy at a given could tailor the payoff contingencies to better price on a given date, find it profitable suit the LDC and potential investors. to the option only in the event that the One such strategy is the call option spread, commodity's market price rises above the strike which would provide a cap on the payout in the price. Thus, an LDC that sells high strike options event of a very high commodity price. A spread incurs an obligation that needs to be fulfilled is conceptually equivalent to the LDC's selling a only if commodity prices increase substantially— call at a given strike price and simultaneously a circumstance in which fulfillment of all obli- buying a call at a higher strike price.13 This com- gations would be easier for the LDC. bination entitles the to an increasing Selecting a high strike price for the call op- payout as the commodity price rises in the range tions enhances the instrument's marketability. between the two strike prices. If the commodity High strike price call options need not be price rises further, though, the cap comes into designated as "senior" obligations (those that play. LDC governments might prefer this ar- must be met in advance of existing debt) in rangement for pol itical reasons. Setting a cap on order to attract buyers. Although call option the contingent liability would also be advan- transactions entail some risk of default, the tageous in the case of agricultural commodities, option's value remains high, even when default for which quantity risks caused by uncertain har- risk and junior designation are taken into con- vests are significant. sideration, because the chance of default is small when the commodity reaches the high strike price. (See the example of option pricing in the box on page 10.) As junior obligations, Supporting Theory option sales would not require approval by existing creditors—an obstacle that frequently As is nowclear, the LDC is not the only party to blocks additional loans to highly indebted bear commodity price risk; the LDC's creditors countries. share that risk. While periods of high prices are Since LDCs would be issuing call options on characterized by large capital inflows and rapid their own export commodities, the countries growth, low prices strain LDC economies and of- would bear little financial risk in meeting their ten result in debt crises as the revenue needed obligations. When calls are covered, the issuer to service outstanding debt dries up. At the same simply sells the available commodity to the time debt held by the LDC's creditors fluctuates option holder for the strike price. When call in value according to the LDC's creditworthi- options are not covered, that is, when the un- ness, which in turn depends on the commodity derlying commodity is not in the possession of price. If the risk of price fluctuation subjects the issuing party, the issuer takes the chance of both the LDC and the creditor to the specter of having to purchase quantities of the commodity default during low-price times, and if default is at high prices to fulfill the contract. costly to the two parties, then some sort of reve- LDCs could either sell covered calls to new nue smoothing is advantageous to both parties. investors or them for a portion of outstand- One way to smooth revenue across high- and ing debt. To ensure a fair price to the LDC for the low-price periods is for the LDC to sell "claims" calls, the sale and distribution could be con- on the high-price period. High strike price op- ducted via a closed-bid auction in a manner tions are exactly such a claim. They allow the similar to the Morgan Guaranty Mexican debt- LDC to transfer money from potential high-price swap of February 1988. LDCs could set a mini- periods into an immediate low-price period. mum acceptable price in advance, or they could According to option pricing theory, the more retain the right to reject low bids. volatile the commodity price is, the more such

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Table 1. Estimated Value of Vulnerable Oil Options For Various Terms and Strike Prices (Johnson-Stulz Pricing Method: Spot Oil Price = $17.25; Oil Price Volatility = 28 percent per year; Initial Pool Value = $10.77 per option; Pool Volatility = 42 percent per year; Correlation between Oil Price and Pool Value = .5; Interest Rate = 8 percent per year)

, . Years until expiration: Strik0 e pnce per barrel 2 3 4 5 6 7

$25 $1.27 $2.01 $2.59 $3.04 $3.39 $3.65 26 1.11 1.83 2.42 2.88 3.23 3.51 27 .96 1.67 2.25 2.72 3.09 3.38 28 .84 1.51 2.10 2.57 2.96 3.25 29 .73 1.44 1.95 2.43 2.84 3.13 30 .63 1.25 1.82 2.30 2.70 3.01 31 .55 1.14 1.69 2.17 2.57 2.89 32 .48 1.04 1.58 2.06 2.46 2.78

an option is worth. Consequently, the use of also accounts for default-risk.18 The box on page LDC covered calls is most feasible in exactly 10 describes the methodology and explains the those cases where it is most necessary. assumptions and parameter values used. With a price of $2.72 for an option on one barrel of Mexican oil, a sale of call options on one year's quantity of oil exports could net Mex- An Example of an LDC Covered Call ico $1.28 billion in current revenue (Table 2). A sale of options on five years' exports would While the features and theoretical underpin- bring $6.4 billion.19 This revenue would be suffi- nings of LDC covered calls are straightforward, a cient to retire 6.37 percent of Mexico's foreign realistic example can clarify the features out- bank debt at face value, and more than 15.9 per- lined. Mexico owes $100.3 billion to foreign cent at current market discounts. By compari- interests.14 Payment of principal and interest son, the recent Mexican financing package ne- exceeded $15 billion in 1988, an amount equal gotiated under the Brady plan framework ex- to 46 percent of export revenues.15 Yet Mexico tinguished $7 billion in commercial bank debt. consistently produces between 880 million and In addition, a fixed reduced interest rate was 1.1 trillion barrels of oil each year. Since 1982 secured on over $22 billion in claims. However, over 470 million barrels per year have been this debt relief was partially offset by new loans exported.16 Proven reserves amount to 70 bil- totaling nearly $ 1.4 billion from banks and about lion barrels. Thus, the supply and production of $5.75 billion from official sources to provide for Mexican oil is reliable. principal repayments and guarantee interest Under conditions prevailing in the second (see Jorge C. Castañeda 1990 and Truell 1990). quarter of 1989, when the market price for Mex- The Mexican government has expressed an in- ican oil stood at $17.25 per barrel, an option to terest in further reducing their commercial bank sell oil five years later at a price of $27 would debt over time, and the revenue raised by the have been worth approximately $2.72 (see proposal presented here could allow such re- Table l).17 This figure is computed using Herb ductions without a drawdown in reserves. Johnson and ReneStulz's (1987) pricing model, The sale of options is not a sale of oil; it which is similar to the Black-Scholes model but merely sets the highest price that Mexico can

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Table 2. Estimated Revenue to Mexico For Issues of Options with Various Terms and Strike Prices (billions of U.S. dollars)

(Based on Johnson-Stulz vulnerable option valuation; assumes options cover 470 million barrels, approximately one year's exports; all other assumptions are as given in Table 1)

Years until expiration: Strike price per barrel 2 3 4 5 6 7

$25 $.60 $.94 $1.20 $1.40 $1.60 $1.70 26 .52 .86 1.10 1.40 1.50 1.70 27 .45 .79 1.10 1.30 1.50 1.60 28 .39 .71 .99 1.20 1.40 1.50 29 .34 .68 .92 1.10 1.30 1.50 30 .30 .59 .86 1.10 1.30 1.40 31 .26 .54 .79 1.00 1.20 1.40 32 .23 .49 .74 .97 1.20 1.30

charge the option purchaser for oil during the Mexico is not the only example of a country expiration year. Should the price of oil remain that could benefit from selling call options on an low, Mexico would be free to sell oil in any man- export commodity. Brazil, for example, could ner it chooses. Only if the price rebounds and sell options on soybeans and coffee. Chile and exceeds the $27 strike price would Mexico be Peru might sell options on copper, Bolivia, tin obliged to sell oil to the option holders for $27 options. Any commodity-exporting country could per barrel. At that price, though, the flow of make use of a similar strategy. Table 4 lists revenue would be sizable, and Mexico's finan- several LDC candidates and their principal cial situation would be greatly improved. In export commodities. either case, the sale of covered calls would pro- vide Mexico with added revenue now, revenue that could be used to ease the current finan- cial crisis. The Proposal from the Table l presents the Johnson-Stulz prices for LDCs' Perspective vulnerable Mexican oil options—that is, those subject to default risk—using various com- A sale of high strike price covered calls would binations of strike prices and maturities. Table 3 provide an LDC with much-needed revenue presents Black-Scholes prices, which assume when revenue is otherwise scarce. Unlike a debt- no default risk but correspond to the same —which involves permanent sale of parameter values. (These parameters are given productive resources, often at depressed prices— in the box and in the tables.) The difference be- the LDC covered call entails no loss of control or tween the Black-Scholes and johnson-Stulz ownership over productive resources. Sale of prices is the , that is, the reduction LDC covered calls, on the other hand, relin- in the value of the option that is due to the risk of quishes only some potential profits for a fixed default. As a percentage of the option price, the amount of time—that is, the difference between credit spread is lower for higher strike prices. the market price of the commodity and the op- The attractiveness of the option is that its con- tion's strike price (if the difference is positive) tingent liability is paid only when funds are for a prespecified quantity of output. plentiful and thus effectively does not compete The obligation would be "costly" to the LDC with existing debt for available funds. in high-price periods because the LDC would

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Table 3. Estimated Value of Default-Free Oil Options For Various Terms and Strike Prices (Black-Scholes Pricing Method: Spot Oil Price = $17.25; Oil Price Volatility = 28 percent per year; Interest Rate = 8 percent per year)

Years until expiration: Strike price per barrel 2 3 4 5 6 7

$25 $1.41 $2.45 $3.47 $4.43 $5.33 $6.18 26 1.23 2.23 3.22 4.17 5.08 5.93 27 1.06 2.02 2.99 3.93 4.83 5.69 28 .92 1.83 2.78 3.71 4.60 5.45 29 .80 1.66 2.58 3.49 4.38 5.23 30 .69 1.51 2.39 3.29 4.18 5.02 31 .60 1.37 2.22 3.11 3.98 4.82 32 .52 1.24 2.07 2.93 3.79 4.63

fulfill its obligation by selling at a lower-than- LDC debt held by the creditors. Although cov- market price; however, that price would be ered calls require no servicing prior to expira- much higher than the market price had been at tion, unlike debt forgiveness, they have inherent the time the option was written. Thus, the trans- value; thus the treatment is more action would still be profitable to the LDC and favorable to banks than is outright debt for- would further enhance its welfare, despite its giveness. obligatory nature. Furthermore, if the LDC had Another advantageous feature of an LDC unused production capacity, exercise of the covered call is its ability to let the investor/ options would provide additional customers creditor share more fully in the fortunes of the and greater total revenue. LDC during times of increasing commodity Should the commodity price not rise above prices. A portfol io of loans to an LDC carries con- the strike price, the option would expire unex- siderable exposure to commodity price risk, but ercised and the LDC would face no further en- offers limited reward should prices rise. LDC cumbrance. In order to supplement income covered calls would grant creditors access to during the continued low-price state, the LDC greater upside potential. Just as commodity might then wish to issue additional covered calls prices are theoretically unbounded, the poten- against another future period's production. tial gain from owning an LDC covered call would be unlimited. Although the option would expire worthless should commodity prices not recover, the same The Proposal from the could be said of LDC debt. Nonperformance on Creditor's Perspective loans is quite possible during the low-price periods in which an option would expire out of Sales of covered calls by LDCs would benefit the money. Thus, LDC debt and LDC covered creditors for several reasons. The new instru- calls have certain downside features in com- ment embodies some attractive investment mon. Certainly there are price scenarios in features. LDCs' selling covered calls represents which LDC debt would perform better than LDC a feasible alternative to demanding new loans covered calls; nevertheless, some creditors/ from creditors. The revenue covered calls pro- investors might prefer the different risk-return vide LDCs would enhance the val ue of the other profile of the option.

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Another potentially attractive feature of LDC Table 4. covered calls could be their greater liquidity relative to LDC bank debt and equity stakes. As Selected Heavily Indebted a standardized , LDC covered calls Countries and Their Chief should be easier to sell than bank debt and Export Commodities equity holdings. Indeed, an active market for LDC covered calls might develop in response to Export Revenue their availability. Banks would then have an from Commodity as a Percent avenue to reduce their LDC exposure, should of Total Exports, they wish to, by swapping bank debt for calls Country Commodity 1982-88 and then selling those calls in the market. The proposal should also appeal to creditors Argentina Wheat 10.8 Corn 7.8 because of the effect it would have on the entire portfolio of LDC investments. The options would Bolivia Natural Gas 49.3 only pay off when LDC funds are plentiful, and Tin 25.1 the initial sale or swap of the options would Brazil Soybeans 9.5 reduce the LDC's debt burden. Hence, the LDC Coffee 8.4 could better service all of its obligations regard- Chile Copper 45.4

less of the behavior of commodity prices. The Colombia Coffee 39.8 LDC would potentially have more funds for de- Fuel Oil 13.4 velopment and thus face enhanced future finan- Ecuador Crude Oil 54.7 cial prospects. Accordingly, the value of all the Bananas 9.4 LDC's outstanding debt could appreciate. Côte d'Ivoire Cocoa Beans 29.7 Clearly, purchase of LDC covered calls is pref- Coffee 18.3 erable to debt forgiveness from the creditors' Mexico Petroleum 57.0 point of view. Like debt forgiveness, selling LDC covered calls would relieve the debtor of some Morocco Phosphates 18.5 debt service obligations and make service of Peru Copper 16.8 remaining debt more manageable. This change Zinc 9.5 would enhance the value of remaining debt, just Philippines Coconut Products 10.8 as debt forgiveness does. By receiving LDC Uruguay Wool 19.7 covered calls, however, creditors would main- 86.0 tain a claim on LDC funds that might become Venezuela Petroleum available at a later date. Furthermore, whereas banks must write off debt that is forgiven, re- Source: International Monetary Fund. ceipt of calls would preserve some capital since LDC covered calls are a valuable asset. worthless, much in the same way an accident insurance policy returns nothing when no acci- dent occurs. During low-price periods, however, The Market for LDC Covered Calls the option owner would continue to enjoy the low price of the essential commodity. Users of the LDC's export commodity face Processors and distributors of oil products, price risk exactly opposite of that borne by the along with the U.S. Department of Energy, which LDC: users suffer when prices are high and pros- purchases oil to supply the nation's strategic per when prices are low. Purchase of an LDC reserves, might be potential buyers of LDC covered call would be a form of insurance covered calls on oil. Agents who wish to specu- against excessive price hikes. It would insulate late on the price of oil might also be interested, the user against severe fluctuations in the com- and they would add liquidity to the market. modity price, thereby facilitating investment Investment managers could use LDC covered planning and marketing decisions. Should the calls to over the long term against the price remain low, the option would expire adverse effects commodity price shocks can

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exert on investment portfolios. Currently, few could offset one another. In this way, LDC instruments are available that allow agents to covered calls could possibly offer creditors and speculate or hedge prices over the long term. debtors a hedge against inflation risk. Logistical details need to be addressed on a case-by-case basis. For instance, to avoid si- multaneous exercise of all options, which would Potential Problems put a tremendous strain on the LDC's ability to deliver the commodity, the option could be This plan is subject to criticism in several written so that a forward delivery contract would areas, and certain details would have to be be sold to the holder, with the delivery date worked out. For example, creditors and inves- determined by the order in which the exercise tors might fear that an LDC would renege on its request is received. obligation should the price of oil rise substan- tially above the option strike price. This be- havior is unlikely, however, since it would be akin to default on a loan. An LDC's initial sale of Conclusions LDC covered calls in order to retire debt would exhibit a willingness to honor international fi- High strike price covered call options are a nancial agreements. For countries striving to do market-oriented solution that should be ex- so during hard times, reneging during easier cir- plored further and given serious consideration cumstances seems unlikely. as a response to the current LDC debt crisis. The LDC would have to bear inflation risk. Because their use offers LDCs a new source of Worldwide inflation over the life of the option revenue without adding to an already difficult might lower the real value of the strike price at debt burden, sale of call options would benefit which the commodity would have to be sold. If both LDCs and the holders of existing LDC debt. this occurred, however, the same inflation that By smoothing income across periods of high and would make fulfillment of the option obligation low commodity prices and providing insurance costl ier to the LDC would also rel ieve the LDC of against periods of excessively high commodity some of its debt burden. Inflation increases the prices, this holds advan- real cost of the option obligation but decreases tages for LDCs, consumers of their export com- the real cost of the debt obligations. As long as modities, and investors. Thus, it presents a the term of the options were similar to or shorter promising new approach to easing debt obliga- than the interval at which banks reprice loans in tions and furthering economic advancement in response to inflation and changing interest highly indebted countries. rates, the two countervailing inflation effects

An Explanation of the Johnson-Stulz Pricing Model

The Johnson-Stulz method is useful for valuing time.1 Therefore, the intrinsic value of the option- "vulnerable" options, that is, options that face that is, the difference between the strike price and some risk of default. The method relies on various the underlying asset price—also moves smoothly. assumptions similar to those required by the Black and Scholes showed that a portfolio consist- Black-Scholes methodology, which is commonly ing of the underlying asset and a short position in used to price exchange-traded and other default- bonds could exactly replicate the option. Because free options. Both models assume that the price of the replicating portfolio and actual option offer the underlying asset (oil in the Mexican example) the same payoff at expiration, theirvalues must be moves randomly and smoothly through time and the same any time before expiration. Otherwise, that the percent change over any instant of time is arbitrage profits could be realized. The Black- independent of the change at any other point in Scholes methodology essentially prices the op-

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tion by adding up the observable prices of the dividing the total pool value by the number of assets in the replicating portfolio. options issued. The Johnson-Stulz method differs from the Table I presents Johnson-Stulz prices for Mex- Black-Scholes method in that it assumes the ican oil options using various combinations of option writer has limited assets available to meet strike prices and maturities. The computation the potential liability of the option. Mexico, for uses data from the second quarter of 1989. The oil example, has a limited pool of funds with which to price was $17.25 per barrel at that time. The total cover its option obligations upon exercise. If the value of the pool was $5.1 billion, or $10.77 per pool value falls below the option obligation, the option if options are issued on one full year's option owners do not receive the full option payoff worth of exports, 470 million barrels. Parameter upon expiration.2 Instead, they receive the avail- inputs were estimated using quarterly data from able funds in the pool. In other words, at expira- 1982 to 1989. The standard deviation of percent tion the vulnerable call pays the minimum of the changes in the pool value is 43 percent per year. option's intrinsic value or its share of the pool (the The volatility of the oil price is 28 percent per total pool divided by the number of options year. issued). The prices in Table 1 may overstate the true In pricing the option used in the example, the value of these options for the following reason: the pool was valued in the following manner: for a oil price may not follow a random walk as the given period, Mexico's current account surplus, Johnson-Stulz, like the Black-Scholes, model as- which was sometimes negative, was added to the sumes. Oil prices may revert to some long-run previous period's foreign currency reserves, and level, which may vary over time. If this were true, required debt service was subtracted.3 This num- the oil prices would not be as variable overtime as ber, however, was often negative since Mexico par- the models predict, and so the computed prices tially financed large trade deficits and debt service would be too high. However, there is no firm by obtaining new loans. To apply the Johnson- empirical evidence that oil prices are mean- Stulz method, it was necessary to adjust the pool, reverting. Nevertheless, the Johnson-Stulz prices, normalizing it to equal zero at the level at which though possibly high, are closer to the true value default would be likely. of the default-risky options than the Black-Scholes The unadjusted pool reached its historical prices. Further modeling research should achieve minimum in the third quarter of 1981; the next more reliable values for these options. year Mexico suspended interest payments. Since The Johnson-Stulz methodology takes into ac- that time the total quantity of foreign debt has count the relationship between the value of the risen. Moreover, both the ratio of debt service to pool and the underlying commodity. When oil GNP and the ratio of external liabilities to GNP prices are high, the funds available to Mexico to have similarly been much higher in several of the service outstanding debt and pay off options are years since the time of the payments moratorium.4 more plentiful. The correlation coefficient be- Thus, the rapid rate of capital outflow, rather than tween these two variables is 0.5, estimated over the excessive level of debt amassed, apparently the sample period running from 1982 to 1989. The was the main factor prompting Mexico's interest higher this correlation, the lower the option de- suspension in 1982. To normalize the pool, there- fault risk will be. A high positive correlation would fore, it was assumed that Mexico would make pay- be expected for countries like Mexico whose ments on the options as long as the pool value economies depend largely on single export com- remained above its historical minimum. If that modities. Thus, high strike price covered call minimum were ever again achieved, it would lead options are attractive instruments for these coun- to default. To normalize the pool in this way, the tries, since the relationship between commodity historical minimum (-$5.4 billion) was subtracted price and the country's financial resources miti- from each entry in the time series of pool values.5 gates default. Finally, the pool per option was computed by

Notes

'More precisely, the asset price is assumed to follow a pricing models. For the sake of greater realism, it diffusion process (a continuous-time geometric Brown- would be desirable to allow discrete jumps in the pro- ian motion). This assumption is standard in option cess, which, for example, might be due to oil price

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shocks. However, such a model poses serious techni- 3Data were provided by the International Monetary cal problems in valuing vulnerable options. These Fund and Banco de Mexico. details will be addressed in future research. 4The Economist Intelligence Unit (19891, 35. 2Since Mexico would own the oil on which the option 5Since this computation involved subtracting a nega- was written, however, a default on the options would tive number, it in effect added to the pool. This entail selling the oil to a third party on the recognizes the historical record that the unadjusted rather than selling to the option owner at the strike pool could become negative without resulting in a price. default.

Notes

'The type of option proposed here is the "European" developing countries amassed current account surpluses option, which cannot be exercised until maturity. totalling $11.9 billion (U.S.) over the five years from 1971 2E. Schwartz (1982) cited two instances where commodity- through 1975. Over the period 1981-86, LDCs amassed linked bonds—which grant the lender the option to take a deficits totaling $242.7 billion (International Monetary given quantity of a commodity instead of the principal at Fund, 1987 Yearbook, 136). maturity—had been issued. O'Hara (forthcoming) de- 9See Schuker (1988), 134. scribed how commodity-linked bonds could be used to l0Latin America's per capita output fell 7 percent in the shift commodity price risk from LDCs to risk-neutral 1980s, whereas it had grown 40 percent in the 1970s. See banks. Many other examples exist. Farnsworth (1990). The "value recovery clause" in the recent Mexican debt 1 'See "LDC Debt News" (1990), 12. package allows banks to receive additional payments l2See Sachs (1989b), 92, and DiLeo and Remolona (1989). starting in 1996 should the price of oil be above $14 per 13In practice, it would not be necessary to issue two options; barrel in constant 1989 dollars by that time. The additional one contingent claim contract can be written with the payments will be subject to a cap proportional to the same features. amount of old loans each bank tenders in exchange for the '"See "Country Risk-Watch," (1989/90), 94-95. new fixed-interest bonds. ,5The World Bank (1989b), 254. ^The World Bank (1989a), 2. l6See Banco de Mexico. 4 LIBOR is the rate of interest on large loans between credit- l7World Oil Price Table, Weekly Petroleum Status Report. worthy international banks. It is commonly used as the l8For a description of the Black-Scholes model, see Black base rate for floating-rate international loans, much in the and Scholes (1973). manner that the prime rate is often used as the base for 19This is the sum of the val ues of five series of options cover- floating rates on loans in the United States. ing export production for the period between three and ^The World Bank (1988), xi. seven years into the future. Three-year options would ^See Schuker (1988), 134. cover the oil to be produced three years from now, four- 7 lbid. year options would cover production four years from now, and so forth.

References

Banco de Mexico. "Indicadores del Sector Externo." In- Durr, Barbara. "Debt, Inflation Continue to Hamper Latin dicadores Economicos, updated monthly. America." Financial Times, December 22, 1989. Black, Fischer, and Myron Scholes. "The Pricing of Options The Economist Intelligence Unit. Mexico: Country Profile, and Corporate Liabilities." journal of Political Economy 1989-90. Annual Survey of Political and Economic Back- 81 (1973): 637-59. ground. London: The Economist Intelligence United Castañeda, )orgeC. "Mexico's Dismal Debt Deal." New York Limited, 1989. Times, February 25, 1990. Farnsworth, Clyde. "U.S. Falls Short on Its Debt Plan for Third "Country Risk-Watch " The International Economy 3 (De- World." New York Times, January 9, 1990. cember 1989/)anuary 1990): 94-95. International Monetary Fund. International Financial Statis- DiLeo, Paul, and Eli M. Remolona. "On Voluntary Conver- tics. Washington, D.C.: IMF, various issues. sions of LDC Debt." Federal Reserve Bank of New York, Johnson, Herb, and René Stulz. "The Pricing of Options with unpublished manuscript, July 24, 1989. Default Risk." Journal of Finance 42 (June 1987): 267-80. Dornbusch, Rudiger. "International Debt and Economic "LDC Debt News." American Banker, March 20, 1990, 12. Instability." Federal Reserve Bank of Kansas City Eco- O'Hara, Maureen. "Financial Contracts and International nomic Review (January 1987): 15-32. Lending." Journal of Banking and Finance (forthcoming).

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Perasso, Giancarlo. "The Pricing of LDC Debt in the Secon- Schwartz, Eduardo. "The Pricing of Commodity Linked dary Market: An Empirical Analysis." Kyklos 42, fasc. 4 Bonds." Journal of Finance 37, no. 2 (1982): 525-39. (1989): 533-55. Truell, Peter. "Mexico, Creditor Banks Complete Pact Cover- Sachs, leffrey. "New Approaches to the Latin American Debt ing $48 Billion of Debt." Wall Street Journal, January 11, Crisis." Essays in International Finance, no. 174. Inter- 1990. national Finance Section, Department of Economics, The World Bank. World Debt Tables, 1987-88: External Debt Princeton University. Princeton, New Jersey, July 1989a. of Devloping Countries. Vol. I, Analysis and Summary . "Making the Brady Plan Work." Foreign Affairs Tables. Washington, D.C., 1988. (September 1989b): 87-104. . World Debt Tables, 1989-90: External Debt of Schuker, Stephen A. American "Reparations" to Germany, Developing Countries. Vol. I, Analysis and Summary 1919-33: Implications for the Third-World Debt Crisis. Tables. Washington, D.C., 1989a. Princeton Studies in International Finance, no. 61. Inter- . World Debt Tables, 1989-90: External Debt of national Finance Section, Department of Economics, Developing Countries. Vol. 2, Country Tables. Washing- Princeton University. Princeton, New Jersey, July 1988. ton, DC., 1989b. Schwartz, Anna J. "International Debts: What's Fact and What's Fiction." Economic Inquiry 27 (January 1989): 1-19.

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