United States, United Kingdom even less or more complete European Union has developed the concept of derivative, used it, gave boom to their economy in a shortest possible time span, Enjoyed its fruits, developed few guide lines, passed through its abuses of over estimation and now a days trying to get this “JIN” into the bottle by implementing further laws, standards and risk mitigation techniques. But we are still unaware even to the very basic concept of derivate. This paper in your hand put some light over few drops named foreign exchange derivative from this great ocean of derivate.
Although wherever In Pakistan the corporate world is involved in derivative transaction but as far as Public Sector is concerned, it’s totally an alien concept. Although wherever the public tax money is involved the caretakers must pay greater attention towards its uses, and must hedge the up-coming risk which could efficiently being forecasted in public sector. The paper in your hand is the first in this series. Case study could be seen in the 3rd paper of this series.
FOREIGN EXCHANGE DERIVATIVE
A Foreign exchange derivative is a financial derivative where the underlying is a particular currency and/or its exchange rate. These instruments are used either for currency speculation and arbitrage or for hedging foreign exchange risk. For detail see the following: 1. Foreign exchange option
2. Forex swap
3. Currency future
4. Currency swap
5. Foreign exchange hedge
6. Binary option: Foreign exchange
1. FOREIGN-EXCHANGE OPTION
In finance, a foreign-exchange option (commonly shortened to just FX option or currency option) is a derivative financial instrument where the owner has the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date.(“Foreign Exchange (FX) Terminologies: Forward Deal and Options Deal" Published by the International Business Times AU on February 14, 2011.) The FX options market is the deepest, largest and most liquid market for options of any kind in the world. Most of the FX option volume is traded over the counter (OTC) and is lightly regulated, but a fraction is traded on exchanges like the International Securities Exchange, Philadelphia Stock Exchange, or the Chicago Mercantile Exchange for options on futures contracts. The global market for exchange-traded currency options was notionally valued by the Bank for International Settlements at $158,300 billion in 2005.
Example
For example a GBPUSD FX option might be specified by a contract giving the owner the right but not the obligation to sell £1,000,000 and buy $2,000,000 on December 31. In this case the pre-agreed exchange rate, or strike price, is 2.0000 USD per GBP (or GBP/USD 2.00 as is the market standard in terms of quoting) and the notionals are £1,000,000 and $2,000,000.
This type of contract is both a call on dollars and a put on sterling, and is often called a GBPUSD put by market participants, as it is a put on the exchange rate; it could equally be called a USDGBP call, but market convention is quote GBPUSD (USD per GBP).
If the rate is lower than 2.0000 come December 31 (say at 1.9000), meaning that the dollar is stronger and the pound is weaker, then the option will be exercised, allowing the owner to sell GBP at 2.0000 and immediately buy it back in the spot market at 1.9000, making a profit of (2.0000 GBPUSD – 1.9000 GBPUSD)*1,000,000 GBP = 100,000 USD in the process. If they immediately exchange their profit into GBP this amounts to 100,000/1.9000 = 52,631.58 GBP.
Terms
Generally in thinking about options, one assumes that one is buying an asset: for instance, you can have a call option on oil, which allows you to buy oil at a given price. One can consider this situation more symmetrically in FX, where one exchanges: a put on GBPUSD allows one to exchange GBP for USD: it is at once a put on GBP and a call on USD.
As a vivid example: people usually consider that in a fast food restaurant, one buys hamburgers and pays in dollars, but one can instead say that the restaurant buys dollars and pays in hamburgers.
There are a number of subtleties that follow from this symmetry.
Ratio of notionals
The ratio of the notionals in an FX option is the strike, not the current spot or forward. Notably, when constructing an option strategy from FX options, one must be careful to match the foreign currency notionals, not the local currency notionals, else the foreign currencies received and delivered don't offset and one is left with residual risk.
Non-linear payoff
The payoff for a vanilla option is linear in the underlying, when one denominates the payout in a given numéraire. In the case of an FX option on a rate, one must be careful of which currency is the underlying and which is the numéraire: in the above example, an option on GBPUSD gives a USD value that is linear in GBPUSD (a move from 2.0000 to 1.9000 yields a .10 * $2,000,000 / 2.0000 = $100,000 profit), but has a non-linear GBP value. Conversely, the GBP value is linear in the USDGBP rate, while the USD value is non-linear. This is because inverting a rate has the effect of , which is non-linear.
Change of numéraire
The implied volatility of an FX option depends on the numéraire of the purchaser, again because of the non-linearity of .
Hedging with FX options
Corporations primarily use FX options to hedge uncertain future cash flows in a foreign currency. The general rule is to hedge certain foreign currency cash flows with forwards, and uncertain foreign cash flows with options.
Suppose a United Kingdom manufacturing firm is expecting to be paid US$100,000 for a piece of engineering equipment to be delivered in 90 days. If the GBP strengthens against the US$ over the next 90 days the UK firm will lose money, as it will receive less GBP when the US$100,000 is converted into GBP. However, if the GBP weaken against the US$, then the UK firm will gain additional money: the firm is exposed to FX risk. Assuming that the cash flow is certain, the firm can enter into a forward contract to deliver the US$100,000 in 90 days time, in exchange for GBP at the current forward rate. This forward contract is free, and, presuming the expected cash arrives, exactly matches the firm's exposure, perfectly hedging their FX risk.
If the cash flow is uncertain, the firm will likely want to use options: if the firm enters a forward FX contract and the expected USD cash is not received, then the forward, instead of hedging, exposes the firm to FX risk in the opposite direction.
Using options, the UK firm can purchase a GBP call/USD put option (the right to sell part or all of their expected income for pounds sterling at a predetermined rate), which will:
· protect the GBP value that the firm will receive in 90 days' time (presuming the cash is received)
· cost at most the option premium (unlike a forward, which can have unlimited losses)
· yield a profit if the expected cash is not received but FX rates move in its favor
Valuing FX options: The Garman-Kohlhagen model
As in the Black-Scholes model for stock options and the Black model for certain interest rate options, the value of a European option on an FX rate is typically calculated by assuming that the rate follows a log-normal process.
In 1983 Garman and Kohlhagen extended the Black-Scholes model to cope with the presence of two interest rates (one for each currency). Suppose that rd is the risk-free interest rate to expiry of the domestic currency and rf is the foreign currency risk-free interest rate (where domestic currency is the currency in which we obtain the value of the option; the formula also requires that FX rates – both strike and current spot be quoted in terms of "units of domestic currency per unit of foreign currency").
Then the domestic currency value of a call option into the foreign currency is
The value of a put option has value
where :
S0 is the current spot rate
K is the strike price
N is the cumulative normal distribution function
rd is domestic risk free simple interest rate
rf is foreign risk free simple interest rate
T is the time to maturity (calculated according to the appropriate day count convention)
and σ is the volatility of the FX rate.
Risk Management
Garman-Kohlhagen (GK) is the standard model used to calculate the price of an FX option, however there are a wide range of techniques in use for calculating the options risk exposure, or Greeks (as for example the Vanna-Volga method). Although the price produced by every model will agree, the risk numbers calculated by different models can vary significantly depending on the assumptions used for the properties of the spot price movements, volatility surface and interest rate curves.
After GK, the most common models in use are SABR and local volatility, although when agreeing risk numbers with a counterparty (e.g. for exchanging delta, or calculating the strike on a 25 delta option) the Garman-Kohlhagen numbers are always used.
2. FOREIGN EXCHANGE SWAP
In finance, a forex swap (or FX swap) is a simultaneous purchase and sale of identical amounts of one currency for another with two different value dates (normally spot to forward)(Ref: Reuters Glossary http://glossary.reuters.com/index.php?title=FX_Swap)
Structure
A forex swap consists of two legs:
· a spot foreign exchange transaction, and
· a forward foreign exchange transaction.
These two legs are executed simultaneously for the same quantity, and therefore offset each other.
It is also common to trade forward-forward, where both transactions are for (different) forward dates.
Uses
By far and away the most common use of FX swaps is for institutions to fund their foreign exchange balances.
Once a foreign exchange transaction settles, the holder is left with a positive (or long) position in one currency, and a negative (or short) position in another. In order to collect or pay any overnight interest due on these foreign balances, at the end of every day institutions will close out any foreign balances and re-institute them for the following day. To do this they typically use tom-next swaps, buying (or selling) a foreign amount settling tomorrow, and then doing the opposite, selling (or buying) it back settling the day after.
The interest collected or paid every night is referred to as the cost of carry. As currency traders know roughly how much holding a currency position will make or cost on a daily basis, specific trades are put on based on this; these are referred to as carry trades.
Pricing
The relationship between spot and forward is as follows:
where:
F = forward rate
S = spot rate
r1 = simple interest rate of the term currency
r2 = simple interest rate of the base currency
T = tenor (calculated according to the appropriate day count convention)
The forward points or swap points are quoted as the difference between forward and spot, F - S, and is expressed as the following:
where r1 and r2 are small. Thus, the absolute value of the swap points increases when the interest rate differential gets larger, and vice versa.
Related instruments
A forex swap should not be confused with a currency swap, which is a much rarer, long term transaction, governed by a slightly different set of rules.
3. CURRENCY FUTURE
A currency future, also FX future or foreign exchange future, is a futures contract to exchange one currency for another at a specified date in the future at a price (exchange rate) that is fixed on the purchase date; see Foreign exchange derivative. Typically, one of the currencies is the US dollar. The price of a future is then in terms of US dollars per unit of other currency. This can be different from the standard way of quoting in the spot foreign exchange markets. The trade unit of each contract is then a certain amount of other currency, for instance €125,000. Most contracts have physical delivery, so for those held at the end of the last trading day, actual payments are made in each currency. However, most contracts are closed out before that. Investors can close out the contract at any time prior to the contract's delivery date.
History
Currency futures were first created in 1970 at the International Commercial Exchange in New York. But the contracts did not "take off" due to the fact that the Bretton Woods system was still in effect. They did so a full two years before the Chicago Mercantile Exchange (CME) in 1972, less than one year after the system of fixed exchange rates was abandoned along with the gold standard. Some commodity traders at the CME did not have access to the inter-bank exchange markets in the early 1970s, when they believed that significant changes were about to take place in the currency market. The CME actually now gives credit to the International Commercial Exchange (not to be confused with the ICE for creating the currency contract, and state that they came up with the idea independently of the International Commercial Exchange). The CME established the International Monetary Market (IMM) and launched trading in seven currency futures on May 16, 1972. Today, the IMM is a division of CME. In the fourth quarter of 2009, CME Group FX volume averaged 754,000 contracts per day, reflecting average daily notional value of approximately $100 billion. Currently most of these are traded electronically.
Other futures exchanges that trade currency futures are Euronext.liffe, Tokyo Financial Exchange and Intercontinental Exchange.
Terms
As with other futures, the conventional maturity dates are the IMM dates, namely the third Wednesday in March, June, September and December. The conventional option maturity dates are the first Friday after the first Wednesday for the given month.
Uses
Hedging
Investors use these futures contracts to hedge against foreign exchange risk. If an investor will receive a cashflow denominated in a foreign currency on some future date, that investor can lock in the current exchange rate by entering into an offsetting currency futures position that expires on the date of the cashflow.
For example, Jane is a US-based investor who will receive €1,000,000 on December 1. The current exchange rate implied by the futures is $1.2/€. She can lock in this exchange rate by selling €1,000,000 worth of futures contracts expiring on December 1. That way, she is guaranteed an exchange rate of $1.2/€ regardless of exchange rate fluctuations in the meantime.
Speculation
Currency futures can also be used to speculate and, by incurring a risk, attempt to profit from rising or falling exchange rates.
For example, Peter buys 10 September CME Euro FX Futures, at $1.2713/€. At the end of the day, the futures close at $1.2784/€. The change in price is $0.0071/€. As each contract is over €125,000, and he has 10 contracts, his profit is $8,875. As with any future, this is paid to him immediately.
More generally, each change of $0.0001/€ (the minimum Commodity tick size), is a profit or loss of $12.50 per contract.
4. CURRENCY SWAP
A currency swap is a foreign-exchange agreement between two parties to exchange aspects (namely the principal and/or interest payments) of a loan in one currency for equivalent aspects of an equal in net present value loan in another currency; see foreign exchange derivative. Currency swaps are motivated by comparative advantage.[1] A currency swap should be distinguished from a central bank liquidity swap.
Structure
Currency swaps are over-the-counter derivatives, and are closely related to interest rate swaps. However, unlike interest rate swaps, currency swaps can involve the exchange of the principal.[1]
There are three different ways in which currency swaps can exchange loans:
1. The simplest currency swap structure is to exchange only the principal with the counterparty at a specified point in the future at a rate agreed now. Such an agreement performs a function equivalent to a forward contract or futures. The cost of finding a counterparty (either directly or through an intermediary), and drawing up an agreement with them, makes swaps more expensive than alternative derivatives (and thus rarely used) as a method to fix shorter term forward exchange rates. However for the longer term future, commonly up to 10 years, where spreads are wider for alternative derivatives, principal-only currency swaps are often used as a cost-effective way to fix forward rates. This type of currency swap is also known as an FX-swap.[2]
2. Another currency swap structure is to combine the exchange of loan principal, as above, with an interest rate swap. In such a swap, interest cash flows are not netted before they are paid to the counterparty (as they would be in a vanilla interest rate swap) because they are denominated in different currencies. As each party effectively borrows on the other's behalf, this type of swap is also known as a back-to-back loan.[2]
3. Last here, but certainly not least important, is to swap only interest payment cash flows on loans of the same size and term. Again, as this is a currency swap, the exchanged cash flows are in different denominations and so are not netted. An example of such a swap is the exchange of fixed-rate US dollar interest payments for floating-rate interest payments in Euro. This type of swap is also known as a cross-currency interest rate swap, or cross-currency swap.[3]
Uses
Currency swaps have two main uses:
· To secure cheaper debt (by borrowing at the best available rate regardless of currency and then swapping for debt in desired currency using a back-to-back-loan).[2]
· To hedge against (reduce exposure to) exchange rate fluctuations.[2]
Hedging example
For instance, a US-based company needing to borrow Swiss francs, and a Swiss-based company needing to borrow a similar present value in US dollars, could both reduce their exposure to exchange rate fluctuations by arranging any one of the following:
· If the companies have already borrowed in the currencies each needs the principal in, then exposure is reduced by swapping cash flows only, so that each company's finance cost is in that company's domestic currency.
· Alternatively, the companies could borrow in their own domestic currencies (and may well each have comparative advantage when doing so), and then get the principal in the currency they desire with a principal-only swap.
Abuses
In May 2011, Charles Munger of Berkshire Hathaway Inc. accused international investment banks of facilitating market abuse by national governments. For example, "Goldman Sachs helped Greece raise $1 billion of off- balance-sheet funding in 2002 through a currency swap, allowing the government to hide debt."[4] Greece had previously succeeded in getting clearance to join the euro on 1 January 2001, in time for the physical launch in 2002, by faking its deficit figures.[5]
History
Currency swaps were originally conceived in the 1970s to circumvent foreign exchange controls in the United Kingdom. At that time, UK companies had to pay a premium to borrow in US Dollars. To avoid this, UK companies set up back-to-back loan agreements with US companies wishing to borrow Sterling.[6] While such restrictions on currency exchange have since become rare, savings are still available from back-to-back loans due to comparative advantage.
Cross-currency interest rate swaps were introduced by the World Bank in 1981 to obtain Swiss francs and German marks by exchanging cash flows with IBM. This deal was brokered by Salomon Brothers with a notional amount of $210 million dollars and a term of over ten years.[7]
During the global financial crisis of 2008, the currency swap transaction structure was used by the United States Federal Reserve System to establish central bank liquidity swaps. In these, the Federal Reserve and the central bank of a developed[8] or stable emerging[9] economy agree to exchange domestic currencies at the current prevailing market exchange rate & agree to reverse the swap at the same exchange rate at a fixed future date. The aim of central bank liquidity swaps is "to provide liquidity in U.S. dollars to overseas markets."[10] While central bank liquidity swaps and currency swaps are structurally the same, currency swaps are commercial transactions driven by comparative advantage, while central bank liquidity swaps are emergency loans of US Dollars to overseas markets, and it is currently unknown whether or not they will be beneficial for the Dollar or the US in the long-term.[11]
The People's Republic of China has multiple year currency swap agreements of the Renminbi with Argentina, Belarus, Hong Kong, Iceland, Indonesia, Malaysia, Singapore, South Korea and Uzbekistan that perform a similar function to central bank liquidity swaps.[12] [13][14]
Currency Swap Example
Company A is doing business in USA, and it has issued a $20 million dollar-denominated bond to investors in the US. Company B is doing business in Europe, and It has issued a bond of $ 15 Million Euros. The two companies can enter into an agreement to exchange the principal and interest of the bonds. The $15 million Euro-denominated bond will be the obligation of company A, and company B will be obligated to the $20 million bond. [15]
References
5. FOREIGN EXCHANGE HEDGE
A foreign exchange hedge (FOREX hedge) is a method used by companies to eliminate or hedge foreign exchange risk resulting from transactions in foreign currencies. This is done using either the cash flow or the fair value method. The accounting rules for this are addressed by both the International Financial Reporting Standards (IFRS) and by the US Generally Accepted Accounting Principles (US GAAP).
Foreign exchange risk
When companies conduct business across borders, they must deal in foreign currencies. Companies must exchange foreign currencies for home currencies when dealing with receivables, and vice versa for payables. This is done at the current exchange rate between the two countries. Foreign exchange risk is the risk that the exchange rate will change unfavorably before the currency is exchanged.
Hedge
A hedge is a type of derivative, or a financial instrument, that derives its value from an underlying asset. This concept is important and will be discussed later. Hedging is a way for a company to minimize or eliminate foreign exchange risk. Two common hedges are forwards and options. A Forward contract will lock in an exchange rate at which the transaction will occur in the future. An option sets a rate at which the company may choose to exchange currencies. If the current exchange rate is more favorable, then the company will not exercise this option.
Accounting for Derivatives
Under IFRS
Guidelines for accounting for financial derivatives are given under IFRS 7. Under this standard, “an entity shall group financial instruments into classes that are appropriate to the nature of the information disclosed and that take into account the characteristics of those financial instruments. An entity shall provide sufficient information to permit reconciliation to the line items presented in the balance sheet”. Derivatives should be grouped together on the balance sheet and valuation information should be disclosed in the footnotes. This seems fairly straightforward, but IASB has issued two standards to help further explain this procedure. The International Accounting Standards IAS 32 and 39 help to give further direction for the proper accounting of derivative financial instruments. IAS 32 defines a “financial instrument” as “any contract that gives rise to a financial asset of one entity and a financial liability or equity instrument of another entity”. Therefore, a forward contract or option would create a finacial asset for one entity and a financial liability for another. The entity required to pay the contract holds a liability, while the entity receiving the contract payment holds an asset. These would be recorded under the appropriate headings on the balance sheet of the respective companies. IAS 39 gives further instruction, stating that the financial derivatives be recorded at fair value on the balance sheet. IAS 39 defines two major types of hedges. The first is a cash flow hedge, defined as: “a hedge of the exposure to variability in cash flows that (i) is attributable to a particular risk associated with a recognized asset or liability or a highly probable forecast transaction, and (ii) could affect profit or loss”. In other words, a cash flow hedge is designed to eliminate the risk associated with cash transactions that can affect the amounts recorded in net income. Below is an example of a cash flow hedge for a company purchasing Inventory items in year 1 and making the payment for them in year 2, after the exchange rate has changed.
Date | Spot Rate | US $ value | Change | Fwd. Rate | US $ value | FV of contract | Change |
12/1/Y1 | $1.00 | $20,000.00 | $0.00 | $1.04 | $20,800.00 | $0.00 | $0.00 |
12/31/Y1 | $1.05 | $21,000.00 | $1,000.00 | $1.10 | $22,000.00 | ($1,176.36) | ($1,176.36) |
3/2/Y2 | $1.12 | $22,400.00 | $1,400.00 | $1.12 | $22,400.00 | ($1,600.00) | ($423.64) |
Cash Flow Hedge Example
12/1/Y1 | Inventory | | $20,000.00 | | To record purchase and A/P of 20000C |
| | A/P | | $20,000.00 | |
12/31/Y1 | Foreign Exchange Loss | | $1,000.00 | | To adjust value for spot of $1.05 |
| | A/P | | $1,000.00 | |
| AOCI | | $1,000.00 | | To record a gain on the forward contract |
| | Gain on Forward Contract | | $1,000.00 | |
| Forward Contract | | $1,176.36 | | To record the forward contract as an asset |
| | AOCI | | $1,176.36 | |
| Premium Expense | | $266.67 | | Allocate the fwd contract discount |
| | AOCI | | $266.67 | |
3/1/Y2 | Foreign Exchange Loss | | $1,400.00 | | To adjust value for spot of $1.12 |
| | A/P | | $1,400.00 | |
| AOCI | | $1,400.00 | | To record a gain on the forward cont. |
| | Gain on Forward Contract | | $1,400.00 | |
| Forward Contract | | $423.64 | | To adjust the fwd. cont. to its FV of $1600 |
| | AOCI | | $423.64 | |
| Premium Expense | | $533.33 | | To allocate the remaining fwd. cont. discount |
| | AOCI | | $533.33 | |
| Foreign Currency | | $22,400.00 | | To record the settlement of the fwd. cont. |
| | Forward Contract | | $1,600.00 | |
| | Cash | | $20,800.00 | |
| A/P | | $22,400.00 | | To record the payment of the A/P |
| | Foreign Currency | | $22,400.00 | |
Notice how in year 2 when the payable is paid off, the amount of cash paid is equal to the forward rate of exchange back in year 1. Any change in the forward rate, however, changes the value of the forward contract. In this example, the exchange rate climbed in both years, increasing the value of the forward contract. Since the derivative instruments are required to be recorded at fair value, these adjustments must be made to the forward contract listed on the books. The offsetting account is other comprehensive income. This process allows the gain and loss on the position to be shown in Net income.
The second is a fair value hedge. Again, according to IAS 39 this is “a hedge of the exposure to changes in fair value of a recognized asset or liability or an unrecognized firm commitment, or an identified portion of such an asset, liability or firm commitment, that is attributable to a particular risk and could affect profit or loss”. More simply, this type of hedge would eliminate the fair value risk of assets and liabilities reported on the Balance sheet. Since Accounts receivable and payable are recorded here, a fair value hedge may be used for these items. The following are the journal entries that would be made if the previous example were a fair value hedge.
Fair Value Hedge Example
12/1/Y1 | Inventory | | $20,000.00 | | to record purchase and A/P of 20000C |
| | A/P | | $20,000.00 | |
12/31/Y1 | Foreign Exchange Loss | | $1,000.00 | | to adjust value for S.R of $1.05 |
| | A/P | | $1,000.00 | |
| Forward Contract | | $1,176.36 | | to record forward contract at fair value |
| | Gain on Forward Contract | | $1,176.36 | |
3/1/Y2 | Foreign Exchange Loss | | $1,400.00 | | to adjust value for S.R. of $1.12 |
| | A/P | | $1,400.00 | |
| Forward Contract | | $423.64 | | to adjust the fwd. contract to its FV |
| | Gain on Forward Contract | | $423.64 | |
| Foreign Currency | | $22,400.00 | | to record the settlement of the fwd. cont. |
| | Forward Contract | | $1,600.00 | |
| | Cash | | $20,800.00 | |
| A/P | | $22,400.00 | | to record the payment of the A/P |
| | Foreign Currency | | $22,400.00 | |
Again, notice that the amounts paid are the same as in the cash flow hedge. The big difference here is that the adjustments are made directly to the assets and not to the other comprehensive income holding account. This is because this type of hedge is more concerned with the fair value of the asset or liability (in this case the account payable) than it is with the profit and loss position of the entity.
Under US GAAP
The US Generally Accepted Accounting Principles also include instruction on accounting for derivatives. For the most part, the rules are similar to those given under IFRS. The standards that include these guidelines are SFAS 133 and 138. SFAS 133, written in 1998, stated that a “recognized asset or liability that may give rise to a foreign currency transaction gain or loss under Statement 52 (such as a foreign-currency-denominated receivable or payable) not be the hedged item in a foreign currency fair value or cash flow hedge”. Based on the language used in the statement, this was done because the FASB felt that the assets and liabilities listed on a company’s books should reflect their historic cost value, rather than being adjusted for fair value. The use of a hedge would cause them to be revalued as such. Remember that the value of the hedge is derived from the value of the underlying asset. The amount recorded at payment or reception would differ from the value of the derivative recorded under SFAS 133. As illustrated above in the example, this difference between the hedge value and the asset or liability value can be effectively accounted for by using either a cash flow or a fair value hedge. Thus, two years later FASB issued SFAS 138 which amended SFAS 133 and allowed both cash flow and fair value hedges for foreign exchanges. Citing the reasons given previously, SFAS 138 required the recording of derivative assets at fair value based on the prevailing spot rate.
References
6. BINARY OPTION
In finance, a binary option is a type of option where the payoff is either some fixed amount of some asset or nothing at all. The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option. The cash-or-nothing binary option pays some fixed amount of cash if the option expires in-the-money while the asset-or-nothing pays the value of the underlying security. Thus, the options are binary in nature because there are only two possible outcomes. They are also called all-or-nothing options, digital options (more common in forex/interest rate markets), and Fixed Return Options (FROs) (on the American Stock Exchange). Binary options are usually European-style options.
For example, a purchase is made of a binary cash-or-nothing call option on XYZ Corp's stock struck at $100 with a binary payoff of $1000. Then, if at the future maturity date, the stock is trading at or above $100, $1000 is received. If its stock is trading below $100, nothing is received.
In the popular Black-Scholes model, the value of a digital option can be expressed in terms of the cumulative normal distribution function.
Non exchange-traded binary options
Binary option contracts have long been available Over-the-counter (OTC), i.e. sold directly by the issuer to the buyer. They were generally considered "exotic" instruments and there was no liquid market for trading these instruments between their issuance and expiration. They were often seen embedded in more complex option contracts.
Since mid-2008 binary options web-sites called binary option trading platforms have been offering a simplified version of exchange-traded binary options. It is estimated that around 30 such platforms (including white label products) have been in operation as of January 2011, offering options on some 70 underlying assets.
Exchange-traded binary options
In 2007, the Options Clearing Corporation proposed a rule change to allow binary options,[1] and the Securities and Exchange Commission approved listing cash-or-nothing binary options in 2008.[2] In May 2008, the American Stock Exchange (Amex) launched exchange-traded European cash-or-nothing binary options, and the Chicago Board Options Exchange (CBOE) followed in June 2008. The standardization of binary options allows them to be exchange-traded with continuous quotations.
Amex offers binary options on some ETFs and a few highly liquid equities such as Citigroup and Google.[3] Amex calls binary options "Fixed Return Options"; calls are named "Finish High" and puts are named "Finish Low". To reduce the threat of market manipulation of single stocks, Amex FROs use a "settlement index" defined as a volume-weighted average of trades on the expiration day.[4] The American Stock Exchange and Donato A. Montanaro submitted a patent application for exchange-listed binary options using a volume-weighted settlement index in 2005.[5]
CBOE offers binary options on the S&P 500 (SPX) and the CBOE Volatility Index (VIX).[6] The tickers for these are BSZ[7] and BVZ,[8] respectively. CBOE only offers calls, as binary put options are trivial to create synthetically from binary call options. BSZ strikes are at 5-point intervals and BVZ strikes are at 1-point intervals. The actual underlying to BSZ and BVZ are based on the opening prices of index basket members.
Both Amex and CBOE listed options have values between $0 and $1, with a multiplier of 100, and tick size of $0.01, and are cash settled.[6][9]
In 2009 Nadex, the North American Derivatives Exchange, launched and now offers a suite of binary options vehicles.[10]. Nadex binary options are available on a range Stock Index Futures, Spot Forex, Commodity Futures, and Economic Events.[11]
Example of a Binary Options Trade
A trader who thinks that the EUR/USD strike price will close at or above 1.2500 at 3:00 p.m. can buy a call option on that outcome. A trader who thinks that the EUR/USD strike price will close at or below 1.2500 at 3:00 p.m. can buy a put option or sell the contract.
At 2:00 p.m. the EUR/USD spot price is 1.2490. the trader believes this will increase, so he buys 10 call options for EUR/USD at or above 1.2500 at 3:00 p.m. at a cost of $40 each.
The risk involved in this trade is known. The trader’s gross profit/loss follows the ‘all or nothing’ principle. He can lose all the money he invested, which in this case is $40 x 10 = $400, or make a gross profit of $100 x 10 = $1000. If the EUR/USD strike price will close at or above 1.2500 at 3:00 p.m. the trader's net profit will be the payoff at expiry minus the cost of the option: $1000 - $400 = $600.
The trader can also choose to liquidate (buy or sell to close) his position prior to expiration, at which point the option value is not guaranteed to be $100. The larger the gap between the spot price and the strike price, the value of the option decreases, as the option is less likely to expire in the money.
In this example, at 3:00 p.m. the spot has risen to 1.2505. The option has expired in the money and the gross payoff is $1000. The trader's net profit is $600.
Black-Scholes Valuation
In the Black-Scholes model, the price of the option can be found by the formulas below.[12] In these, S is the initial stock price, K denotes the strike price, T is the time to maturity, q is the dividend rate, r is the risk-free interest rate and σ is the volatility. Φ denotes the cumulative distribution function of the normal distribution,
and,
Cash-or-nothing call
This pays out one unit of cash if the spot is above the strike at maturity. Its value now is given by,
Cash-or-nothing put
This pays out one unit of cash if the spot is below the strike at maturity. Its value now is given by,
Asset-or-nothing call
This pays out one unit of asset if the spot is above the strike at maturity. Its value now is given by,
Asset-or-nothing put
This pays out one unit of asset if the spot is below the strike at maturity. Its value now is given by,
Foreign exchange
If we denote by S the FOR/DOM exchange rate (i.e. 1 unit of foreign currency is worth S units of domestic currency) we can observe that paying out 1 unit of the domestic currency if the spot at maturity is above or below the strike is exactly like a cash-or nothing call and put respectively. Similarly, paying out 1 unit of the foreign currency if the spot at maturity is above or below the strike is exactly like an asset-or nothing call and put respectively. Hence if we now take rFOR , the foreign interest rate, rDOM , the domestic interest rate, and the rest as above, we get the following results.
In case of a digital call (this is a call FOR/put DOM) paying out one unit of the domestic currency we get as present value,
In case of a digital put (this is a put FOR/call DOM) paying out one unit of the domestic currency we get as present value,
While in case of a digital call (this is a call FOR/put DOM) paying out one unit of the foreign currency we get as present value,
and in case of a digital put (this is a put FOR/call DOM) paying out one unit of the foreign currency we get as present value,
Skew
In the standard Black-Scholes model, one can interpret the premium of the binary option in the risk-neutral world as the expected value = probability of being in-the-money * unit, discounted to the present value.
To take volatility skew into account, a more sophisticated analysis based on call spreads can be used.
A binary call option is, at long expirations, similar to a tight call spread using two vanilla options. One can model the value of a binary cash-or-nothing option, C, at strike K, as an infinitessimally tight spread, where Cv is a vanilla European call:[13][14]
Thus, the value of a binary call is the negative of the derivative of the price of a vanilla call with respect to strike price:
When one takes volatility skew into account, σ is a function of K:
The first term is equal to the premium of the binary option ignoring skew:
is the Vega of the vanilla call; is sometimes called the "skew slope" or just "skew". Skew is typically negative, so the value of a binary call is higher when taking skew into account.
C = Cnoskew − Vegav * Skew
Relationship to vanilla options' Greeks
Since a binary call is a mathematical derivative of a vanilla call with respect to strike, the price of a binary call has the same shape as the delta of a vanilla call, and the delta of a binary call has the same shape as the gamma of a vanilla call.
Interpretation of prices
In a prediction market, binary options are used to find out a population's best estimate of an event occurring - for example, a price of 0.65 on a binary option triggered by the Democratic candidate winning the next US Presidential election can be interpreted as an estimate of 65% likelihood of him winning.
In financial markets, expected returns on a stock or other instrument are already priced into the stock. However, a binary options market provides other information. Just as the regular options market reveals the market's estimate of variance (volatility), i.e. the second moment, a binary options market reveals the market's estimate of skew, i.e. the third moment.
In theory, a portfolio of binary options can also be used to synthetically recreate (or valuate) any other option (analogous to integration), although in practical terms this is not possible due to the lack of depth of the market for these relatively thinly traded securities.
References
