Currency Risk In Project Finance
DISCUSSION PAPERCurrency Risk in Project FinanceWim Verdouw (IMG Rebel), David Uzsoki and Carlos Dominguez OrdonezAugust 2015In developed and developing countries alike, thereis a very large need for infrastructure investmentas existing infrastructure ages, economiesdevelop and populations grow. According to theMcKinsey Global Institute, in order to keep upwith projected global GDP growth, the world willneed to invest an estimated 57 trillion between2015 and 2030 (Dobbs et al., 2013). For mostcountries, relying on state budgets alone will notbe sufficient to meet such large investment needs.Public-private partnerships (PPPs), in whichgovernments work together with the private sectorto develop and finance infrastructure, can thereforeplay an important role. In developing countries,international financing institutions (IFIs), such asthe International Finance Corporation (IFC), andother multilateral development banks often helpfinance key infrastructure projects, predominantlythrough hard currency loans. Without theparticipation of IFIs, international commercialbanks would typically be hesitant to participate inthe financing of such projects. However, due to thenature of the international floating exchange rateregime, hard currency loans create currency risk,which in turn results in uncertainty and potentialadditional liabilities for the receiving countries. Toavoid this situation, local currency financing wouldbe preferable but may not always be available.This paper analyzes the impacts of currency risk oninfrastructure projects in developing markets andidentifies ways that currency risk can be managed.It then proposes a two-pronged strategy for IFIsto address the issue of currency risk, focusing onimproving local capital markets and developinglocal currency financing solutions. Based on thisstrategy, the paper then analyzes various financialtools that IFIs can use to stimulate local currencyfinancing in order to help countries meet theirdevelopment goals while limiting their exposure tocurrency risk.1. Currency risk in project financeHard currency loans can create a currency riskif revenues are in local currency. For example, apower plant in India may be financed in dollars,but if electricity tariffs are in rupees, this createsan asset-liability currency mismatch. If the rupeedepreciates against the dollar by 10 per cent,revenues remain unchanged but the liabilities arenow 10 per cent higher. One of the key challengesin project finance in emerging and frontier marketsis to determine who should assume this currencyrisk.In PPPs, an optimal risk allocation generally meansthat a risk should be allocated to the party that isbest positioned to manage or bear that risk, or morespecifically, the party that can accept the risk atthe lowest costs. However, regarding currency riskin these markets, this optimal risk allocation maynot be so straightforward. A typical private sectordeveloper has no influence over the exchange rate. 2015 International Institute for Sustainable DevelopmentIISD.org1
Although the central bank has some control overthe exchange rate through its monetary policies, thegovernment’s effective control of the exchange ratemay be limited. As a result of the above, unhedgedcurrency risk is largely unmanageable for theprivate sector and may be beyond the control ofthe government agency in charge of infrastructuredevelopment, which means that it may not be easilyacceptable for either party.Developers and investors have no control overthe exchange rate and will therefore try to eithermanage the risk (see below for risk managementstrategies) or price the exchange rate risk in theirrates/tariffs. As currency risk can also have anupside (or lower downside than expected), it couldcreate a windfall for the developers/investors. Fromthe lenders’ perspective, beyond receiving interestpayments on the principal, there is no potentialfor upside. Lenders will therefore typically notaccept any significant currency risk and expectthe developer to ensure that any currency risk theproject may assume will not affect its debt service.Given the inherent uncertainties in exchange raterisk and the lack of a predetermined logical riskallocation to either the government or the privatesector, currency risk can be a difficult and sensitivetopic in negotiations between the private sectordeveloper and the government. Furthermore, theuncertainty that currency risk inherently carriesmay undermine one of the key advantages ofPPPs, which is the relative cost certainty achievedthrough long-term contracts. Besides the technicalcomplexity of exchange rate risk and lack of costcertainty, there can also be an important perceptionissue: if the procuring agency—and thereforeultimately the public— directly bears the currencyrisk and observes how the local currency paymentfor the same service significantly increases yearafter year, it may conclude that the project’s foreignfinanciers must be making excessive returns. Inreality, the foreign financiers may be making anormal risk-adjusted return on their hard currencyinvestments and/or loans.2. Managing currency riskThere are a number of strategies to managecurrency risk. However, it should be recognizedupfront that these strategies are typically costly toone of the parties involved: the project developer,financiers, or government. When negotiatingcontracts with private sector developers,governments (or publicly owned utilities) needto acknowledge the real cost of hard currencyfinancing, which includes both the cost of capitalin hard currency and the cost of currency risk thatthe developer is expected to assume. Text box 1contains a variety of currency risk strategies thatcan be used to manage currency risk.Text Box 1: Currency risk management strategies(Partial) Natural hedgeTo reduce the asset-liability currency mismatch that occurs when using foreign currency financing for localservice delivery, a developer may choose to sell a portion or all of the project’s output to a country with thesame currency as its liabilities. For example, the Nam Theun 2 hydropower project in Laos is partially financedby Thai banks through Thai baht–denominated loans and also exports a significant proportion of its energyproduction to Thailand (Multilateral Investment Guarantee Agency [MIGA], 2006). As a result, the Thai baht–denominated loans are not exposed to currency risk. A similar structure has been adopted by Bhutanesehydropower projects that export their production to India, where both debt and the power purchase agreementare in Indian rupees.Local currency swapUnder a currency swap, two parties agree to exchange principal and/or interest payments of a loan in onecurrency for an equivalent loan in another currency. Such swaps allow lenders/borrowers and investors to hedge(a part of) their loans/investments. However, for some emerging and many frontier markets, currency swaps arenot commercially available. The IFC can provide currency swaps for a number of these markets. Furthermore,the Currency Exchange Fund (TCX) is a special purpose fund that can provide currency hedge products for localborrowers in frontier and less liquid emerging markets.IISD DISCUSSION PAPERCurrency Risk in Project FinanceIISD.org2
Text Box 1: Currency risk management strategies (continued)Exchange rate–indexed contractsIf a project’s revenues are indexed to the exchange rate, a currency swap is effectively built in to the contract.As a result, the currency risk is transferred to the buyer, often a state utility or government entity. While thisstrategy solves the currency risk for the developer and financiers, it does not solve the issue for the buyer/government. For example, for highway concessions in Chile, the government has provided an exchange rateguarantee for the dollar-denominated financing component, which effectively translates the local currencypayment mechanism into a hard currency payment mechanism (Lorenzen, Barrientos, & Babbar, 2001).Foreign currency loan under pegIf a country’s currency is pegged to a foreign currency, a developer could consider taking out a loan in theforeign currency, assuming that the peg is maintained. However, a currency risk continues to exist, as the pegmay be undone. This risk ultimately depends on the underlying economic fundamentals and political will tosupport the peg. Pegs exist in many countries, including 13 African countries that use the CFA franc, whichis pegged to the euro. Many Caribbean countries are pegged to the U.S. dollar, whereas Bhutan and Nepal’scurrencies are pegged to the Indian rupee.As can be observed from the currency riskmanagement strategies described in text box 1,most of these strategies are ultimately costly to theend user, as they will most likely need to pay forthe service, either directly (through rates/tariffs) orindirectly (taxation). One way to avoid currencyrisk altogether is to only use local currencyfinancing. However, given the often limited capacityof local currency financing markets, this approachmay not be feasible without outside support. In theremainder of the paper, we will discuss ways thatIFIs can help address the challenges of currencyrisk and local currency financing.3. Local currency financingstrategies for internationalfinancing institutionsIFIs actively participate in infrastructure projectswith private sector involvement in emerging andfrontier markets, predominantly by providing hardcurrency loans. Through their participation, IFIshelp provide comfort to international commercialbanks, which may result in additional infrastructureproject financing. This is an important contributionto developing these countries, as very substantialinvestments in infrastructure are required.However, by providing hard currency loans, IFIsalso create significant currency risk, as discussedabove. Rather than providing hard currencyloans—which are ultimately approximately asexpensive as local currency loans when currencyIISD DISCUSSION PAPERCurrency Risk in Project Financerisk is considered—this paper argues that IFIsshould focus on 1) developing local capital marketsand 2) supporting local currency financing ofinfrastructure projects, preferably through local andinternational commercial banks.It is important to acknowledge that IFIs havealready taken significant steps to support localmarkets. For example, to date IFC has providedover 12 billion in local currency financing throughloans, swaps, guarantees, risk-sharing facilities,and other structured and securitized products(IFC, 2014a). However, IFC’s total disbursedloan portfolio of 24.4 billion in 2014 containedonly 3.2 billion, or 13 per cent, in local currency–denominated products, with the remainder inU.S. dollars ( 18 billion) and euros ( 3.2 billion).Some of the projects supported by IFC do ofcourse generate hard currency revenues, whichin turn do not result in currency risk. Dependingon the exact nature of the project (e.g., localelectricity production versus oil export), localcurrency financing may be more appropriate.Considerable efforts are also being made toimprove local capital markets. Nonetheless, byfocusing specifically on their additionality and onaddressing missing markets and repairing marketfailures in the first place, IFIs can create even morevalue by encouraging commercial banks to financeinfrastructure projects in emerging markets.Develop local capital marketsAccording to Thiam Hee Ng, a senior economistat the Asian Development Bank (ADB)’s OfficeIISD.org3
of Regional Economic Integration, liquidity istightening across Asia, yielding great potentialfor local currency bond markets to fill the gap(Gilmore, 2014). IFIs can help develop localcapital markets in general by providing supportto government through upstream policy work ontopics such as financial regulation, sound monetaryand fiscal policies, strong and independentfinancial government institutions, improved marketinformation, credit reporting systems, and collateralregistries. This kind of support helps create a morerobust financial system that is more likely to beable to provide the long-term financing requiredfor infrastructure projects. This upstream workis essential and makes good use of IFIs’ globalexposure and knowledge base.IFIs also support local financial intermediariesby directly providing credit and equity. Throughthese financial intermediaries, IFIs can extendlonger-term local currency financing to localentrepreneurs and (infrastructure) projects.The mere act of providing local financing—thusavoiding currency risk for local entrepreneurs—isin itself commendable. However, it may also bea suboptimal use of IFIs’ financial resources andan underuse of international commercial banks.Instead of providing direct financial support, IFIsshould identify and address the missing marketsand market failures that cause these financialintermediaries to not have access to sufficientcapital in the first place. These may be linked toa variety of risks, including project, political andcurrency risks. By providing credit enhancementsor guarantees to (international) commercial debtand equity providers, IFIs can leverage the privatesector’s resources and increase the overall accessto local currency capital. IFIs already provide suchguarantee products, but they typically representa small proportion of the total balance sheet. Forexample, non-trade guarantees represented less than2 per cent of IFC’s total 2014 commitments (IFC,2014a).Besides increasing the total financial resourcesavailable to local financial intermediaries (andtherefore to local entrepreneurs and projects),the above approach also helps create morecomprehensive and efficient capital marketsthat may, over time, require lower levels ofguarantees and hence can help countries transitionIISD DISCUSSION PAPERCurrency Risk in Project Financetowards more sustainable financing solutions. Bysignificantly rebalancing their portfolio towardcredit enhancement and guarantee products, IFIscan create more value in emerging and frontiermarkets.Support local currency financingAlthough developing local capital markets is anessential step, it does not preclude direct financingof infrastructure projects by foreign financiers.This is particularly relevant when local capitalmarkets are not sufficiently developed or simply donot have enough domestic savings to finance largeinfrastructure projects. Indeed, prudent regulationsrelated to local bank portfolio diversificationcan limit the total pool of funds obtainable fromlocal banks. For example, Nepal is said to haveonly enough domestic savings to finance a singlemedium-sized hydropower plant, but its needsare much higher. In cases such as these, foreigninvestment may be the only immediate solution tofinancing an infrastructure project. As mentionedearlier, IFIs often play a very important role infinancing such projects through direct loans, whichare largely in hard currency. These loans in turncreate a currency risk. When providing these hardcurrency loans to local infrastructure projects, IFIsmust acknowledge that the real cost of finance isapproximately the same as local currency financing.The advantage of this type of IFI financing mainlycomes in the form of potentially longer tenures andthe “stamp of approval” effect, which may convinceother (international) financiers to participate.Related to the point made above regarding directsupport to local financial intermediaries, directlending or investment by IFIs to infrastructureprojects may in fact be a suboptimal use of theirfinancial resources. Following the outlined approachof replacing direct lending with guarantees, IFIscan leverage international commercial banks andmake more efficient use of their own financialresources. Furthermore, as IFIs sometimes provide“concessional”—below market rate—financing,IFIs could use the value of this effective subsidy toabsorb (some of) the currency risk, thus loweringthe cost of currency risk to infrastructure projects.Transition to new IFI financing approachIn order to adopt the above approach, in whichdirect lending is replaced with guarantee products,IISD.org4
IFIs will initially have to actively seek outcommercial financial intermediaries to partner with,as missing markets and/or market failures havelargely kept them from getting involved. As IFIsincreasingly shift their focus from direct lendingand financing to providing guarantee products,commercial banks will need to be informed andactively encouraged to take part in projects thatpreviously would have been mainly financed byIFIs. Furthermore, governments and developers inemerging and frontier markets need to be advisedon these shifting priorities in order to prepare themto more actively engage with (international anddomestic) commercial banks. The guarantees tobe provided by IFIs will ensure that the projects’residual risk profile (in terms of project, currencyand political risk) is acceptable to commercialfinanciers. Typically, (international) financiers maybe comfortable with project risk but will most likelyneed additional comfort on currency and politicalrisk.We will use the remainder of this paper to discussvarious products and services IFIs can employ toefficiently develop local capital markets and supportlocal currency financing.4. Financial tools to stimulate localcurrency financingIFIs have a wide range of financial tools availableto them to support the development of local capitalmarkets and to encourage local currency financing.The following recommendations can be customizedto the particular needs of the target country in linewith the current state of its capital markets.Support local currency bond issuanceFixed income securities such as bonds constitutea significant part of capital markets worldwide.While governments in many emerging marketshave frequently used bonds to borrow frominternational capital markets, their use in raisingcapital for private sector infrastructure projectshas been limited, in part due to country risks. Thisis especially the case for local currency bonds, asthe additional currency risk, or the high cost ofhedging, makes these debt instruments unattractiveto international investors. Recognizing thatbond financing can be an efficient and relativelyIISD DISCUSSION PAPERCurrency Risk in Project Financeeconomical way to raise local currency capital(notwithstanding drawbacks such as inflexibilityand expensive breakage), IFIs are providingdifferent credit enhancement solutions to improvethe risk-return profile of these securities. Throughthe guarantee of an AAA-rated institution suchas the IFC, these bond issues can obtain a creditrating that is not only appealing to investors, butalso helps decrease the cost of financing (i.e., yield).When it comes to providing support to bondfinancing, IFIs should focus on local currency bondissues as opposed to foreign currency bonds. Byincreasing the available local currency offerings,IFIs not only eliminate currency risk but alsoplay an important role in developing local capitalmarkets. Through the issuance of local currencybonds, IFIs can help build the financial andregulatory environment that is necessary for a wellfunctioning, robust local capital market. During theissuing process, shortcomings of current marketregulations can be identified and adjusted, buildingon international best practices.Local currency bond issues also help extend therange of investable local financial instruments,which is key for increasing the participation ofmarket players, as local investors need to have asufficient variety of securities to be able to makeefficient asset allocation decisions matching theirrisk-return profiles and time horizon. In addition,IFIs should aim to support deals with sufficientissue size to attract institutional investors andjustify bond issue transaction costs. IFIs have thenecessary capacity and international expertise tohelp establish a capital market environment thatallows other international or domestic issuers toraise capital in local currency. Increased marketparticipation results in better liquidity, which hasmany positive spillover effects on the domesticeconomy. Most importantly, the cost of financingwill decrease for local companies and projects.For many, this will create the first opportunityto borrow directly from capital markets, as theirsize made tapping international capital marketspreviously impossible.IFC’s five-year Umuganda bond issued in Rwanda(2014, 12.25 per cent yield) is a recent example ofIFIs issuing local currency bonds (IFC, 2015a). Asper IFC’s vice president and treasurer, JingdongIISD.org5
Hua, the “Umuganda bond will support thedevelopment of the country’s capital marketsso they can intermediate savings and privatesector investment” (IFC, 2014b). A wide rangeof investors, both domestic and international,participated in the issue.As explained above, under the approach proposedin this paper, IFIs could use their resourceseven more efficiently by providing the requiredguarantees to overcome missing markets andmarket failure and let commercial financialinstitutions issue future local currency bonds.An interesting example of this is IFC’s recentlyimplemented guarantee program in Indonesia. Inthis program, financial support was offered throughboth direct loans for green-field projects and a 20per cent credit guarantee for a 500 billion Indonesiarupiah bond (approximately 39 million) (IFC,2015b). For the later operation, IFC used only 8million of the total amount of resources designatedfor the program, while direct loans accountedfor more than 780 million. As the example alsoshows, guarantees typically still represent a smallshare of IFIs’ commitments, with the lion’s sharestill being direct lending. A more efficient use ofIFIs’ resources would further increase the use ofguarantees, potentially resulting in longer-tenorlocal currency bonds.Support derivatives markets to provide localcurrency hedging instrumentsCurrency hedging instruments such as foreignexchange forwards and swaps play a substantialrole in facilitating international transactions. Asexplained earlier, without appropriate hedging,exchange rate fluctuations can significantly affectthe bankability of any infrastructure project thatrelies on foreign financing. However, in manymarkets, basic currency hedging instrumentsare not available. In other cases, some form ofderivatives market may exist, but there is nomeaningful liquidity to trade these securities.Alternatively, the market may be too thin, resultingin very large bid/offer spreads, making hedginguneconomical. On the one hand, this meansthat local businesses and financial institutionswith access to international capital markets facea currency risk when sourcing foreign currencyfinancing. On the other hand, without theIISD DISCUSSION PAPERCurrency Risk in Project Financepossibility to hedge their currency exposure,international investors and IFIs will be hesitant tomake investments or lend in local currency.The availability of foreign exchange derivatives istherefore essential for a well-functioning economyand capital market. IFIs should play an activerole in facilitating the trading of these financialinstruments by acting as market makers, providingpricing and sufficient liquidity in currency pairs forwhich trading would otherwise not take place or forwhich the market is too illiquid. The interventionwould achieve significant short-term as well aslong-term impacts, including a better-functioninglocal currency market with increased availabilityof (foreign-source) long-term financing for vitalinfrastructure projects.For currency pairs that currently cannot behedged, IFIs should help create hedging products.An example of this is the TCX. Its mandate isto develop better-functioning capital markets indeveloping countries by providing currency riskmanagement products for exotic currencies (TCX,2013). However, its services are only available toits investors (mainly IFIs) and their clients andthe country limits can easily be exceeded by onesingle large transaction. One of its main principlesis additionality, so TCX only gets involved ifno adequately priced commercial alternative isavailable. Also, its services can only be used forhedging purposes, not for speculation. If IFIsindeed start using their considerable financialresources to replace direct lending by guaranteesthat may also cover currency risk, they will need tosimultaneously help grow initiatives like TCX.Support domestic financial institutions inaccessing long-term liquidityAvailability of easily accessible, affordablefinancing is an essential requirement for economicdevelopment and stable growth. In emerging andfrontier markets, bank loans typically constitutethe main source of financing for the private sector.However, due to the asset liability mismatch (shortterm deposits, long-term liabilities), commercialbanks may struggle to provide long-term financingas typically required for infrastructure projects. Thismismatch challenge is all the more real for banksin emerging and frontier markets, resulting in theavailability of only relatively short loan maturities.IISD.org6
Furthermore, local banks’ low credit rating andthe volatile domestic economic and politicalenvironment make longer-term internationalfinancing expensive and sometimes simplyinaccessible. Even if some type of borrowing fromforeign sources is possible, the financial institutionmay struggle to hedge the underlying currency risk.Infrastructure projects require exactly the type offinancing that banks in emerging markets typicallylack the most: large size with long-term maturity.Along with high domestic interest rates, this mayhelp explain the continuous reliance on IFIswhen it comes to infrastructure project finance.IFIs’ assistance has definitely helped realizenumerous vital pieces of infrastructure, providingmuch-needed economic boost and meaningfulsocial impact. However, direct IFI financing tothese projects inevitably creates competition forlocal financial institutions, which under idealcircumstances would provide the lending to avoidcurrency risk.IFIs should therefore redirect their support in away that reinforces local capital markets, and morespecifically domestic banks, so that they are able tofill their important role as local currency lendersin the infrastructure space. IFIs could address theissue of unavailability of long-term financing tolocal banks by offering solutions that are specificallyaimed at remedying this lack of long-term liquidity.Their intervention could be in the form of adirect credit line to local banks for infrastructureprojects. However, it would be more efficientand therefore preferable to provide the requiredguarantees to enhance the ability of local banksto raise capital from international markets. Thiswould not only solve the long-term financing issues,but would also encourage local banks to build inhouse expertise and know-how while improvingtheir international reach and credibility. Buildingsufficient in-house expertise and a dedicated projectfinance desk requires experienced staff, who needto be recruited and provided with sufficientlyinteresting perspectives. For a local bank (as wellas international banks acting locally) to justifyinvesting in developing such a team requires a solidproject pipeline, which in turn depends on a longterm commitment by both IFIs and governmentsto use local financing for infrastructure projectdevelopment. If this commitment exists and localIISD DISCUSSION PAPERCurrency Risk in Project Financebanks can indeed raise international financing todevelop their project finance portfolio, internationalcommercial banks can gain more exposure to localbanks, hence improving overall international capitalmarkets.Develop and provide credit enhancementsAs explained in the previous sections, guaranteesand credit enhancement can play an importantrole in IFIs’ strategy to develop local capitalmarkets and increase local currency financing.These mechanisms can help transfer specific risksfrom investors and lenders to guarantee providers.Through the intelligent use of guarantees andcredit enhancements, projects can be de-risked,making them more attractive for both domestic andinternational financiers. Ultimately, the questionfor IFIs should be what exact risks need to betransferred through these instruments to meetdomestic and international financiers’ requirementsto finance infrastructure projects in emerging andfrontier markets. IFIs should strive to identify theserisks and where necessary and appropriate provideguarantees for them. If properly implemented, IFIswould not be required to provide direct lending andcan focus only on addressing missing markets andmarket failures.In order to identify what risks should be transferred,a distinction can be made between currency risk,political risk, and project risks, with the latter beingdefined as any risk that is not currency or politicalrisk. An example of project risk would be thevariation in annual energy production from a solarpower plant or higher than anticipated operatingcosts of a toll road.Currency riskInternational financiers can use the existingcurrency hedging instruments described aboveto provide local currency financing to projectdevelopers and local financial intermediaries.As the effective cost of hard currency borrowing(hard currency interest rate plus cost of hedging)is typically close to the cost of local currencyborrowing, projects should be financially feasibleunder the effective cost of borrowing. If no hedginginstruments exist for a given currency pair, or ifit has insufficient liquidity and depth, IFIs shouldsupport the development of such derivatives, asIISD.org7
explained earlier. If a project is of particular socialand/or economic importance, a government or IFIcould consider assuming some of the currency riskto lower the ultimate cost of financing. However,for either the host government or IFIs to providea (partial) guarantee for the
Text Box 1: Currency risk management strategies (continued) Exchange rate-indexed contracts If a project's revenues are indexed to the exchange rate, a currency swap is effectively built in to the contract. As a result, the currency risk is transferred to the buyer, often a state utility or government entity. While this
Transaction currency The currency in which a transaction originates. Accounting currency The primary currency in which a legal entity maintains its financial records. The accounting currency is stored in the Ledger table. Reporting currency The reporting currency of the ledger. The reporting currency is stored in the Ledger table. It is optional.
the currency of the bond's denomination as the local currency and the chosen currency of the portfolio or index as the base currency. The return of this security in the base currency on day t can be computed using the following inputs. and 1 are the market values in local currency at the close of day t and t-1 respectively.
Currency Harvest was 15.22%. The Global currency harvest returned 12.07% and the G10 Currency harvest returned 8.02%. The Sharpe ratios for the Balanced Currency Harvest, Global Currency Harvest and G10 Currency Harvest over the period were 1.60, 1.23 and 1.07 respectively. (The returns are in USD terms
a sterling/Euro currency account held with us.) Each payment up to the currency equivalent of 100 Free Each payment over the currency equivalent of 100 6 Sterling and foreign currency payments payable to an account held with us in a different currency from the payment Each payment up to 100 or the currency equivalent of 100 Free
Currency Exchange Setup. Adding Currency Code and Exchange Rates2-1. Editing Currency Exchange Rate2-2. Removing Currency Exchange Rate2-2. Commission Charge Code and Account2-2. Setting Up Commission Charge Code2-4. Setting up System Account2-4. Performing Currency Exchange Transaction. Buy Sell Currency Exchange3-1. Exchange Charge to Account3-2
from an underlying asset which in foreign currency options is the exchange rate. There are two types of foreign currency options, a call currency option and a put currency option. A call option on a particular currency gives the holder the right but not an obligation to buy that currency at a predetermined exchange rate at a particular date and .
A "convertible" virtual currency is a virtual currency that has an equivalent value in real currency, or acts as a substitute for real currency. It usually has a measurable value in real money and what makes it convertible lies in its ability to exchange for real currency based on its determinable value in the market.
Andreas M unch and Endre S uli Mathematical Institute, University of Oxford Andrew Wiles Building, Radcli e Observatory Quarter, Woodstock Road Oxford OX2 6GG, UK Barbara Wagner Weierstrass Institute Mohrenstraˇe 39 10117 Berlin, Germany and Technische Universit at Berlin, Institute of Mathematics Straˇe des 17. Juni 136 10623 Berlin, Germany (Communicated by Thomas P. Witelski) Abstract .
