Nelkin 6870 Term Paper

As the world continues to expand into a global marketplace, business between corporations of different nations and engaging in foreign investment have both become extremely prevalent.  Due to this increased involvement in international markets, currency markets have also taken on a greater importance.  As currency markets have grown over the years and as companies have begun to take a greater interest in involvement outside of their individual nation, ways to protect against the added risks involved with international trade have come about.  One of the largest risks that emerges out of doing business away from home is the introduction of foreign exchange rate risk, which involves the potential depreciation of one’s own currency relative to the currency of one’s customers or producers.  In order to provide a method of protection from these risks, currency derivates were developed. 

Currency derivatives take several forms, including forward contracts, futures contracts, option contracts, swap contracts or even hybrids of two of these, such as futures option contracts or swaptions.  Each of these derivatives offers its own set of advantages and disadvantages relative to the others, and therefore each one has certain scenarios where it is the best choice.  In general there are two categories an investor in derivatives can fall into; they are either a hedger or a speculator.  “Hedgers use currency derivatives to reduce the risk of international trade” (Hopper, 3).  These are primarily corporations that engage in business outside of their home country and are faced with potential risks associated with exchange rates.  The other group of investors is known as speculators.  “Speculators use derivatives to increase substantially the potential return on their investments” (3).  Hedgers and speculators or an investor who is a combination of the two make up the majority of investors in the currency derivatives market.  The pricing of currency derivatives is a topic that is important to both of these types of investors and is a question that in some cases is still being debated today.  This paper will discuss the different types of currency derivatives, who the primary users of each derivative are, how and when they should ideally be used, the advantages and disadvantages involved with each type, and the different pricing methods used for each of them. 

            The first and simplest type of currency derivative is a forward contract.  “A forward contract is an agreement to buy or sell a specific quantity of currency at a predetermined dollar price on a specific date in the future” (4).  Forward contracts are used in order to set up a specific purchase or sale in the future at a price at which will be acceptable based upon the information that one has today.  Forward contracts are agreements that are made in what is called the “over-the-counter” market, meaning that they are individualized contracts that are unregulated and specific to each instance.  The nature of a forward contract makes it a very illiquid asset, and because of this characteristic, these contracts are very rarely entered into by individuals or speculators.  Forward contracts are primarily used by larger institutions in order to protect future earnings and eliminate exchange rate risk.  “Forwards reduce the risk of loss by locking in the future exchange rate” (4).  Forward contracts are not always guaranteed to be beneficial.  If the exchange rate moves against the investor who is long in the contract, then the investor will face losses from the forward contract.  However, seeing as forwards are typically used as devices for hedging, these losses will be counteracted by gains in the investment they were intended to protect.  “Another problem with forward contracts is that they involve potentially large credit risk” (4).  Since these contracts are not exchange traded and are unregulated there is no clearinghouse to ensure payment, creating a default or credit risk.  In most instances, those who engage in forward contracts are not likely to default, for they are usually companies and the counterparties who involve themselves in the contract are quite often banks who require deposits; however, the nature of a forward contract still leaves the possibility of default as a potential risk.  As a derivative, forward contracts provide an easily customized opportunity for hedging against exchange rate risk, which provides users with an opportunity that cannot be found in other standardized currency derivatives.

            Another type of currency derivative is a futures contract, which is very similar to a forward contract, but has several key differences.  Like a forward contract, a futures contract involves a promise to buy or sell a currency at a specified price at a certain date in the future.  However, “futures contracts, unlike forward contracts, are traded on organized exchanges” (5).  This quality of a futures contract gives it a characteristic that makes it much more attractive than a futures contract, liquidity.  Since they are traded on an exchange, futures contracts do not have the same default risk that forward contracts have, for the exchange acts as a clearinghouse for the contract and can ensure its fulfillment.  In addition to being exchange traded, another “difference is that profits or losses from holding a futures contract are realized and paid out at the end of the day” (5).  This process is called being marked to market, and makes the returns on futures contracts seem very different from those of a forward contract.  Futures contracts are commonly used in a similar manner to forwards; they are used for hedging by corporations who are afraid of exchange rate risk. 

The key issue that comes into play when trying to enter into a currency futures contract is how is should be valued.  Most futures contracts are for commodities and in these instances “theoretical futures prices of carry commodities are based on the cash-and-carry model” (Bell, 69); however, with currency futures, there is no underlying asset, so the model does not apply exactly.  When looking at the cost-of-carry model, “in addition to interest cost, models of commodity futures pricing include storage and convenience costs” (McAleer, 278).  In order to adapt this model, the storage and convenience costs must be removed and “the carrying costs are essentially domestic and foreign risk-free rates of interest” (278).  Black’s model is the standard cost-of-carry hypothesis applied to currency futures; however, “Black’s discussion is correct only when the interest rate is constant over time” (Doffou, 566).  In a study of the risk premium and cost-of-carry hypotheses for currency futures contracts, the results of the study provided “substantial support for the cost-of-carry hypothesis” (McAleer, 287). 

Although the cost-of-carry hypothesis that was put forth by Black is one of the most widely used and many believe it to be adequately accurate, several other methods of pricing futures contracts also exist.  “Sundaresan provides a valuation of futures contracts in a general equilibrium framework where futures prices depend on the preferences of the agents in the economy” (Doffou, 566).  This model differs from the Black model in two main aspects. First, it is based on a general equilibrium, while the Black’s cost-of-carry formula values futures contracts in a partial equilibrium.  Second, Sundaresan’s model bases futures contracts prices on the preferences of agents in the economy, while the Black model is based upon the costs involved with holding the asset over a certain period. 

Another well known economist, Fama, presented a model based upon risk premiums.  “Fama argued that, under market efficiency and rational expectations, the forward (futures) exchange rate is equal to the expected future spot rate plus a risk premium” (McAleer, 278).  In comparison to the previous models presented, the model put forth by Fama can be likened to the Black model by intuitively comparing the risk premium to the domestic and foreign interest rate; however, typically when valuation is done, the risk premium is typically understood to be the return above the risk-free rate.  Fama’s model can also be easily tied to Sundaresan’s model, for the preferences of the agents in the economy when valuing the futures contract could most certainly be associated with the risk premium they demand above the expected future spot rate. 

The simplest of all methods for the valuation of futures contracts comes from Thomas, who argues that “if the spot price is a random walk, then today’s spot price is the best predictor of the futures spot price” (Bell, 69).  In this argument, Thomas essentially states that there is no pattern to currency futures prices, for they are random, and therefore the only information that exists in order to predict the price in the future is the exchange rate today.  If Thomas’s assumption is correct, then a trader should buy whenever the futures price falls below the spot price and sell whenever the futures price rises above the spot price.  In contrast with Thomas’s base idea, a study of mean aversion and return predictability in currency futures declares that “in a market with heterogeneous participants including rational traders and uninformed noise traders, asset prices may reflect irrational bubbles or fads resulting in the violation of the random walk hypothesis” (Elyasiani, 9).  The idea behind the random walk hypothesis is that prices are completely random, so if traders no longer engage in the random trading they supposedly typically take part in and begin to follow a fad, they create a bubble that will cause the random walk hypothesis to no longer be acceptable. 

Another model that has been studied in order to estimate futures prices involves the application of cointegration theory.  “The basic insight into cointegration analysis is that, although many economic series are nonstationary, groups of such nonstationary variables may move together in the long run” (McAleer, 279).  The application of cointegration theory would look for long run relationships that can be found between the spot prices and currency futures prices.  “The presence of such cointegrating relationships has been observed in financial futures markets” (279).  Although the idea of a continuous long term pattern that provides adequate predictive ability as to currency futures prices would be very useful, the long term nature of the data and general unpredictability of the currency futures markets that comes out of the large number of driving forces involved, cause the use of cointegration theory to price currency futures to seem inadequate. 

Although there are numerous methods available for the pricing of futures, the Black model still remains the most widely used and taught of them all.  The principles involved with futures contract pricing using the Black model seem the most logical and most applicable.  Another source of its acceptability may come from its relation to the pricing models we use for other derivatives also, for it is based on the same principles and uses the same concepts as commodity futures pricing and ideologically resembles other pricing models. 

A third type of commonly used currency derivative is the option.  “A currency option gives its holder the right, but not the obligation, to take a position on a specific quantity of foreign currency at a prearranged price on or before the date the option expires” (Hopper, 7).  In essence, a currency option acts exactly like a stock option except that rather than having a strike price at which the underlying asset, the stock, can be bought or sold, a currency option has a set exchange rate at which the foreign currency can be traded.  “A currency option is a kind of currency insurance: the option insures against unfavorable exchange rate movements, so that the maximum loss one can experience is the premium paid for the option” (7).  In this aspect, a currency option acts exactly like a hedge in order to ensure that a specific desired exchange rate is at least met.  Currency options are seemingly more often used as speculative devices than the other currency derivatives.  It has been shown that “information-based trading explains more of the trading volume in currency options on the US dollar/British pound exchange rate than hedging” (Sarwar, 698).  This may be due to the nature of options themselves, for many other derivatives are more concrete contracts requiring possible future commitments and payments, while an option contract is exactly that, an option.  The nature of currency options contracts is also responsible for the fact that “currency options are more attractive to informed trades than are the currency markets owing to the higher leverage available in the options market” (683).

As with futures contracts, options are not simple to price, for it is difficult to put a value on what the opportunity to do something is worth.  One model that is used in pricing currency options is the Garman-Kohlhagen model.  This model is “actually only an adaptation of the ordinary Black-Scholes model for stock options” (Ekvall, 41).  In the Garman-Kohlhagen (modified Black-Scholes) model, the spot exchange rate simply replaces the stock price and the foreign interest rate is included as an additional variable.  However, it is important to note that “a number of studies have, in fact, provided evidence on mispricing of currency options by the Garman-Kohlhagen model” (41).  In several models that incorporated stochastic interest rates and jump processes, there was little change in the predicted price; therefore “stochastic volatility option pricing models have been developed to allow for the impact of changing volatility on option prices” (266).  One such option pricing model that diverges from the modified Black-Scholes model is Heston’s stochastic volatility model.  “The stochastic volatility option pricing models attempt to improve the pricing of options by allowing for a non-zero skewness and for higher kurtosis than is allowable in the log-normal distribution of the Black-Scholes model” (Krehbiel, 267). 

In a study on empirical performance of alternative pricing models of currency options, the modified Black-Scholes model and Heston’s stochastic volatility model were compared in several respects.  First of all, the study inquired into the effect of variable interest rates which are a source of pricing errors in the modified Black-Scholes model.  The study concluded that “the stochastic volatility process of the model may have captured the impact of variable interest rates on currency option prices” (286).  This conclusion comes from the nonexistence of interest rate differential bias found in the data and correlates with the conjecture from the Nobel Prize winning economist, Merton, that “the stochastic volatilities result in part from variable interest rates” (286).  A second dimension that was explored in the study was the existence of pricing biases in the option pricing models.  In the area of pricing biases, the stochastic volatility model once again proved to be more accurate than the modified Black-Scholes model.  “The only bias that exists for the stochastic volatility model in the aggregate sample is the moneyness bias.  In contrast, the prices for the modified Black-Scholes model exhibits the moneyness bias, volatility bias and the interest rate differential bias” (289).  The third area which the study delved into was the pricing performance.  This section was examined using regression tests of the degree of association between the actual prices and model-based prices.  As it turned out, “the Black-Scholes model with daily-revised volatilities is somewhat better than the stochastic volatility model in predicting the actual option prices” (283).  The results of the study showed that the two models were fairly equal across the aggregate sample and that “the main advantage of the stochastic volatility model over the modified Black-Scholes model for the present sample of options is in eliminating some of the well-known pricing biases of the Black-Scholes model” (289). 

When compared to other currency derivatives, options have their strong and weak points.  “In contrast to a forward contract, [one] can benefit from favorable movements in the exchange rate when using options” (Hopper, 4).  This result comes from the fact that in a forward contract the investor is already committed to an exchange rate, while with a currency option, an investor will receive the difference between the options exchange rate and the real exchange rate.  More importantly, the decision to use currency options is more directly related to the decision of using futures contracts than to forwards.  In most instances, currency futures are the main competitor of currency options. 

In deciding which currency derivative to use, one must take into consideration the goal trying to be achieved along with the level of risk and return one wants to receive.  As a tool intended for hedging by corporations, “the empirical results indicate that currency futures contracts serve as a better hedging instrument than currency options” (Hsin, 706).  The conclusion drawn from these results though may also be skewed.  A problem with comparing the hedging effectiveness of an option with that of a futures contract is that “as options are designed to eliminate extreme downside risk, which is one-sided, comparisons based upon variance which is a two-sided risk measure, are biased against options” (Lien, 160).  Volatility is the primary source of risk measurement in financial markets, and therefore a fair comparison of currency futures contracts and currency option contracts is very difficult to achieve. 

It is also important to take into account the costs associated with each derivative when choosing one over the other.  “Corporate managers prefer to hedge the downside risk using futures rather than options, citing the large transaction cost in option trading as the main reason” (160).  The preference of the corporate managers to avoid the large transaction cost is intelligent, for “upon taking into account the transaction cost, futures have a larger excess return per unit than options” (160).  Based upon the evidence of options effectiveness in eliminating risk in relation to cost, options do not seem to be the ideal instrument to hedge with in most situations.  Actually, “the only situation in which options outperform futures occurs when the individual hedger is optimistic and not too concerned about large losses” (168-169).  In such a scenario, the trader is not a hedger, but essentially a speculator.  When one is not attempting to achieve gains in such a manner, the trader becomes a hybrid between a hedger and a speculator.  Due to this evidence, it seems safe to conclude that futures are far more effective instruments for hedging, while options are more attractive and provide greater opportunity for speculation.

In addition to forwards, futures and options, another newer form of derivative that exists is a swap contract.  A swap contract involves the exchanging of payment streams between participants and has often been referred to as a portfolio of forward contracts.  Swaps can take two primary forms, interest rate swaps and currency swaps.  Currency swaps are based upon exchange rates, while interest rate swaps are typically derived from LIBOR, the London interbank offered rate.  Both of these two forms are used to protect from similar risk factors, but they do so in their respective manners. 

When looking at the potential uses of a currency swap contract, the nature of the contract in itself clearly predisposes it to be used primarily for hedging.  First of all, it is designed to facilitate the exchange of future cash flows between currencies, which is not an activity conducive to speculation.  Secondly, a currency swap contract is a derivative that takes place on far too large of a scale for almost any speculator.  In addition to the standard version, swap contracts can also take different forms that are know as exotic swaps: such as a collapsible swap, which a firm can cancel if interest rates turn against it or quanto swaps, which let firms get a floating payment in another currency.  Swap contracts, like forward contracts, are traded over-the-counter, making them easy to specialize to one’s particular needs, but once again, like forward contracts, because swap contracts are not traded on an exchange, they face a default risk. 

When discussing the risks involved with swaps, several advantages and disadvantages come to mind.  When trying to calculate the risk of a swap, it is important to remember that “the interaction of foreign exchange risk and default risk is crucial to credit risk assessments for a currency swap” (Usmen, 44).  Swaps typically have very low credit risk; this aspect of a swap is due to the fact that “the notional amount is not at risk [therefore] a $1 billion swap has less credit risk than a $1 billion bond or loan.” (Haubrich, Page Number).  In most cases, default risk is also very low because the “Interest Rate and Currency Exchange Agreement issued by the International Swap Dealer’s Association contains a provision that makes the defaulting party liable for full payment of amounts due under contract, as well as for additional compensation to cover the future loss of the other party, as long as it is solvent” (Usmen, 48).  This provision helps to eliminate a great deal of default risk and essentially makes nonpayment “indistinguishable from closing out the contract or marking to market” (48). 

Swap contracts can be used for a number of different purposes.  Some of the uses of swap contracts include, “managing the balance sheet and matching asset and liability cash flows, obtaining finer terms in raising new finance, restructuring the balance sheet around existing asset and liability structures, exploiting arbitrage opportunities, or separating risks to enable more effective risk management of the individual risk components” (Helliar, 65).  Swaps can also be used at a national level in order to protect a country.  “China and Malaysia signed a $1.5 billion currency swap agreement…[and] China has also signed currency swap deal with South Korea, Thailand, and Japan to make foreign-exchange reserves available at short notice to a country facing a rapid deterioration in its balance of payments and whose currency is under attack” (Anonymous, 30).  The use of swaps to protect oneself from risk in international trade is vast and effective, from a small business to the protection of a national economy.

Since a swap is more straightforward agreement between two parties with specified payment levels and light risk, and because swaps have unique method of application compared other derivatives, such as being used to denominate profits and costs in the same currency, there is far less disagreement about the proper method to value a swap contract.  There are two basic methods for finding the value of a swap contract.  “The market value of a currency swap is found by assessing the present value of the prospective cash flows in each of the respective currencies” (Kawaller, 46).  A swap contract is also known as a portfolio of forward contracts and therefore it makes sense that “an alternative method of valuing a swap contract is to treat it as the sum of a series of forward rate agreements” (Gupta, 243).  Both of the two methods for valuation of a swap contract are simple and to the point, without any disagreements about any variables, and therefore they are much simpler to choose between and use.

In comparison to other derivatives, swaps occupy a unique niche that the others cannot quite emulate; however, the use of swaps does overlap with the use of other derivatives on some occasions.  As concluded earlier, options contracts are used more often for speculation, while swap contracts are designed primarily for hedging; therefore, a comparison of the two would not be useful or effective.  On the other hand, futures and forward contracts both serve similar functions to swap contracts and therefore can be compared.  Although swap contracts are very similar to forward contracts, there is one key difference, their length.  “Currency swaps are superior to forwards and futures for hedging medium and long-term exposures and eliminate the rolling over of forward contracts” (Evans, Page Number).  In addition to being able to hedge effectively for longer periods of time, currency swaps also have the advantage of being able to “protect users from the risk of changes in the spreads between forward and spot exchange rates” (Same Page Number).  The ability to provide the additional protection from the risk of the spreads expanding or contraction is a characteristic exclusive to a swap contract. 

One of the key differences between futures and forward contracts also creates an additional advantage for a swap contract.  Since a swap contract is actually a series of forward contracts, and because futures contracts are marked-to-market daily, this difference between futures and forwards creates a convexity bias in swap contracts.  “The price-yield relationship for the short swap position exhibits positive convexity; i.e. the price increases more when yields falls than the price falls when yields rise” (Gupta, 244).  One final key relationship between swap contracts and futures contracts is explained in an analysis of swaps and the Eurocurrency futures markets.  “The Eurocurrency futures markets and the interest rate swap markets are intimately linked to each other” (240).  This conclusion is supported by the logic that traders who are involved in swap positions almost always use the Eurocurrency futures market to create a hedge.  In relation to other derivatives, swaps are a more effective and safer method of hedging when it comes to large-scale and long-term international cash flows.

Conclusion….