Currency Options Theta,Vega,Gamma,Delta

A currency option is a contract between a buyer and a seller that gives the buyer the right, but not the obligation, to trade a specific amount of currency at a predetermined price and within a predetermined period of time, regardless of the market price of the currency; and gives the seller, or writer, the obligation to deliver the currency under the predetermined terms, if and when the buyer wants to exercise the option.

Currency options are unique trading instruments, equally fit for speculation and hedging. Options allow for a comprehensive customization of each individual strategy, a quality of vital importance for the sophisticated investor. More factors affect the option price relative to the prices of other foreign currency instruments. Unlike spot or forwards, both high and low volatility may generate a profit in the options market. For some, options are a cheaper vehicle for currency trading. For others, options mean added security and exact stop-loss order execution.

Currency options constitute the fastest-growing segment of the foreign exchange market. As of April 1998, options represented 5 percent of the foreign exchange market. (See Figure 3.1) The biggest options trading center is the United States, followed by the United Kingdom and Japan. Options prices are based on, or derived from, the cash instruments. Therefore, an option is a derivative instrument. Options are usually mentioned vis-a-vis insurance and hedging strategies. Often, however, traders have misconceptions regarding both the difficulty and simplicity of using options.

There are also misconceptions regarding the capabilities of options. In the currency markets, options are available on either cash or futures. It follows, then, that they are traded either over-the-counter (OTC) or on the centralized futures markets.

The majority of currency options, around 81 percent, are traded overthe- counter. (See Figure 3.3) The over-the-counter market is similar to the spot or swap market.

Corporations may call banks and banks will trade with each other either directly or in the brokers' market. This type of dealing allows for maximum flexibility: any amount, any currency, any odd expiration date, any time. The currency amounts may be even or odd. The amounts may be quoted in either U.S. dollars or foreign currencies.

Any currency may be traded as an option, not only the ones available as futures contracts. Therefore, traders may quote on any exotic currency, as required, including any cross currencies.

The expiration date may be quoted anywhere from several hours to several years, although the bulk of dates are concentrated around the even dates—one week, one month, two months, and so on. The cash market never closes, so options may be traded literally around the clock. 

Trading an option on currency futures will entitle the buyer to the right, but not the obligation, to take physical possession of the currency future. Unlike the currency futures, buying currency options does not require an initiation margin. The option premium, or price, paid by the buyer to theseller, or writer, reflects the buyer's total risk.

However, upon taking physical possession of the currency future by exercising the option, a trader will have to deposit a margin.

Seven major factors have an impact on the option price:

1. Price of the currency.
2. Strike (exercise) price.
3. Volatility of the currency.
4. Expiration date.
5. Interest rate differential.
6. Call or put.
7. American or European option style.

The currency price is the central building block, as all the other factors are compared and analyzed against it. It is the currency price behavior that both generates the need for options and impacts on the profitability of options.

The impact of the currency price on the option premium is measured by delta, the first of the Greek letters used to describe aspects of the theoretical pricing models in this discussion of factors determining the option price.

Delta

Delta, or commonly A, is the first derivative of the option-pricing model
Delta may be viewed in three respects:

• as the change of the currency option price relative to a change in the currency price. For instance, an option with a delta of 0.5 is expected to move at one half the rate of change of the currency price. Therefore, if the price of a currency goes up 10 percent, then the price of an option on that particular currency is expected to rise by 5 percent.
• as the hedge ratio between the option contracts and the currency futures contracts necessary to establish a neutral hedge. Therefore, an option with a delta of 0.5 will need two option contracts for each of the currency futures contracts.
• as the theoretical or equivalent share position. In this case, delta is the number of currency futures contracts by which a call buyer is long or a put buyer is short. If we use the same example of the delta of 5, then the buyer of the put option is short half a currency futures contract.

Traders may be unable to secure prices in the spot, forward outright, or
futures market, temporarily leaving the position delta unhedged. In order to
avoid the high cost of hedging and the risk of unusually high volatility, traders
may hedge their original options positions with other options. This method of
risk neutralization is called gamma or vega hedging.

Gamma

Gamma (Г) is also known as the curvature of the option. It is the second derivative of the option-pricing model and is the rate of change of an option's delta, or the sensitivity of the delta. For instance, an option with delta = 0.5 and gamma = 0.05 is expected to have a delta = 0.55 if the currency rises by 1 point, or a delta = 0.45 if the currency decreases by 1 point.
Gamma ranges between 0 percent and 100 percent. The higher the gamma, the higher the sensitivity of the delta. It may therefore be useful to think of gamma as the acceleration of the option relative to the movement of the
currency.

Vega

Vega gauges volatility impact on the option premium. Vega (<;) is the sensitivity of the theoretical value of an option to a change in volatility. For instance, a vega of 0.2 will generate a 0.2 percent increase in the premium for each percentage increase in the volatility estimate, and a 0.2 percent decrease in the premium for each percentage decrease in the volatility estimate.

The option is traded for a predetermined period of time, and when this time expires, there is a delivery date known as the expiration date. A buyer who intends to exercise the option must inform the writer on or before expiration. The buyer's failure to inform the writer about exercising the option frees the writer of any legal obligation. An option cannot be exercised past the expiration date.

Theta

Theta (T), also known as time decay, occurs as the very slow or nonexistent movement of the currency triggers losses in the option's theoretical value.

For instance, a theta of 0.02 will generate a loss of 0.02 in the premium for each day that the currency price is flat. Intrinsic value is not affected by time, but extrinsic value is. Time decay accelerates as the option approaches expiration, since the number of possible outcomes is continuously reduced as the time passes.

Time has its maximum impact on at-the-money options and its minimum effect on in-the-money options. Time's effect on out-of-the-money options occurs somewhere within that range. Bid-offer spreads in the market may make it too expensive to sell the option and trade forward out rights.

If the option shifts deeply into the money, the interest rate differential gained by early exercise may exceed the value of the option. If the option amount is small or the expiration is close and the option value only consists of the intrinsic value, it may be better to use the early exercise.

Due to the complexity of its determining factors, option pricing is difficult. In the absence of option pricing models, option trading is nothing but inefficient gambling.

The one idea to make option pricing is that the option of buying the domestic currency with a foreign currency at a certain price x is equivalent to the option of selling the foreign currency with the domestic currency at the same price x. Therefore, the call option in the domestic currency becomes the put option in the other, and vice versa.

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Futures Market

Currency futures are specific types of forward outright deals which occupy in general a small part of the Forex market (See Figure 3.1). Becausethey are derived from the spot price, they are derivative instruments. They are specific with regard to the expiration date and the size of the trade amount. Whereas, generally, forward outright deals—those that mature past the spot delivery date—will mature on any valid date in the two countries whose currencies are being traded, standardized amounts of foreign currency futures mature only on the third Wednesday of March, June, September, and December.

There is a row of characteristics of currency futures, which make them attractive. It is open to all market participants, individuals included. This is different from the spot market, which is virtually closed to individuals - except high net-worth individuals—because of the size of the currency amounts traded. It is a central market, just as efficient as the cash market, and whereas the cash market is a very decentralized market, futures trading takes place under one roof. It eliminates the credit risk because the Chicago Mercantile Exchange Clearinghouse acts as the buyer for every seller, and vice versa. In turn, the Clearinghouse minimizes its own exposure by requiring traders who maintain a non-profitable position to post margins equal in size to their losses.

Moreover, currency futures provide several benefits for traders because futures are special types of forward outright contracts, corporations can use them for hedging purposes. Although the futures and spot markets trade closely together, certain divergences between the two occur, generating arbitraging opportunities. Gaps, volume, and open interest are significant technical analysis tools solely available in the futures market. Yet their significance extrapolates to the spot market as well.

Because of these benefits, currency futures trading volume has steadily attracted a large variety of players.

For traders outside the exchange, the prices are available from on-line monitors. The most popular pages are found on Bridge, Telerate, Reuters, and Bloomberg. Telerate presents the currency futures on composite pages, while Reuters and Bloomberg display currency futures on individual pages shows the convergence between the futures and spot prices.

Forward Market

The forward currency market consists of two instruments: forward outright deals and swaps. A swap deal is unusual among the rest of the foreign exchange instruments in the fact that it consists of two deals, or legs. All the other transactions consist of single deals. In its original form, a swap deal is a combination of a spot deal and a forward outright deal.

Generally, this market includes only cash transactions. Therefore, currency futures contracts, although a special breed of forward outright transactions, are analyzed separately.

According to figures published by the Bank for International Settlements, the percentage share of the forward market was 57 percent in 1998 (See Figure 3.1). Translated into U.S. dollars, out of an estimated daily gross turnover of US$1.49 trillion, the total forward market represents US$900 billion.

In the forward market there is no norm with regard to the settlement dates, which range from 3 days to 3 years. Volume in currency swaps longer than one year tends to be light but, technically, there is no impediment to making these deals. Any date past the spot date and within the above rangmay be a forward settlement, provided that it is a valid business day for both currencies. The forward markets are decentralized markets, with players around the world entering into a variety of deals either on a one-on-one basis or through brokers. In contrast, the currency futures market is a centralized market, in which all the deals are executed on trading floors provided by different exchanges.

Whereas in the futures market only a handful of foreign currencies may be traded in multiples of standardized amounts, the forward markets are open to any currencies in any amount. The forward price consists of two significant parts: the spot exchange rate and the forward spread. The spot rate is the main building block. The forward price is derived from the spot price by adjusting the spot price with the forward spread, so it follows that both forward outright and swap deals are derivative instruments. The forward spread is also known as the forward points or the forward pips. The forward spread is necessary for adjusting the spot rate for specific settlement dates different from the spot date. It holds, then, that the maturity date is another determining factor of the forward price. Just as in the case of the spot market, the left side of the quote is the bid side, and the right side is the offer side.

Spot Market

Currency spot trading is the most popular foreign currency instrument around the world, making up 37 percent of the total activity.

The fast-paced spot market is not for the fainthearted, as it features high volatility and quick profits (and losses). A spot deal consists of a bilateral contract whereby a party delivers a specified amount of a given currency against receipt of a specified amount of another currency from a counterparty, based on an agreed exchange rate, within two business days of the deal date. The exception is the Canadian dollar, in which the spot delivery is executed next business day.

The name "spot" does not mean that the currency exchange occurs the same business day the deal is executed. Currency transactions that require same-day delivery are called cash transactions. The two-day spot delivery for currencies was developed long before technological breakthroughs in information processing.

This time period was necessary to check out all transactions' details among counterparties. Although technologically feasible, the contemporary markets did not find it necessary to reduce the time to make payments. Human errors still occur and they need to be fixed before delivery. When currency deliveries are made to the wrong party, fines are imposed.

In terms of volume, currencies around the world are traded mostly against the U.S. dollar, because the U.S. dollar is the currency of reference. The other major currencies are the euro, followed by the Japanese yen, the British pound, and the Swiss franc. Other currencies with significant spot market shares are the Canadian dollar and the Australian dollar.

In addition, a significant share of trading takes place in the currencies crosses, a non-dollar instrument whereby foreign currencies are quoted against other foreign currencies, such as euro against Japanese yen.

There are several reasons for the popularity of currency spot trading.Profits (or losses) are realized quickly in the spot market, due to market  volatility. In addition, since spot deals mature in only two business days, the time exposure to credit risk is limited. Turnover in the spot market has been increasing dramatically, thanks to the combination of inherent profitability and reduced credit risk. The spot market is characterized by high liquidity and high volatility. Volatility is the degree to which the price of currency tends to fluctuate within a certain period of time. Free-floating currencies, such as the euro or the Japanese yen, tend to be volatile against the U.S. dollar.

In an active global trading day (24 hours), the euro/dollar exchange rate may change its value 18,000 times. An exchange rate may "fly" 200 pipsin a matter of seconds if the market gets wind of a significant event. On the other hand, the exchange rate may remain quite static for extended periods of time, even in excess of an hour, when one market is almost finished trading and waiting for the next market to take over. This is a common occurrence toward the end of the New York trading day. Since California failed in the late 1980s to provide the link between the New York and Tokyo markets, there is a technical trading gap between around 4:30 pm and 6 pm EDT. In the United States spot market, the majority of deals are executed between 8 am and noon, when the New York and European markets overlap (See Figure 3.2). The activity drops sharply in the afternoon, over 50 percent in fact, when New York loses the international trading support. Overnighttrading is limited, as very few banks have overnight desks. Most of the banks send their overnight orders to branches or other banks that operate in the active time zones.

The major traders in the spot market are the commercial banks and the investment banks, followed by hedge funds and corporate customers. In the interbank market, the majority of the deals are international, reflecting worldwide exchange rate competition and advanced telecommunication systems. However, corporate customers tend to focus their foreign exchange activity domestically, or to trade through foreign banks operating in the same time zone. Although the hedge funds' and corporate customers' business in foreign exchange has been growing, banks remain the predominant trading force.

The bottom line is important in all financial markets, but in currency spot trading the antes always seem to be higher as a result of the demand from all around the world.

The profit and loss can be either realized or unrealized. The realized profit and loss is a certain amount of money netted when a position is closed. The unrealized profit and loss consists of an uncertain amount of money that an outstanding position would roughly generate if it were closed at the current rate. The unrealized profit and loss changes continuously in tandem with the exchange rate.

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