GLOBAL
TABLE OF CONTENTS Introduction Delta Delta as Hedge Ratio Gamma Other Letters Appendix 3 4 5 7 9 10 HIGH RISK WARNING: Before you decide to trade either foreign currency ( Forex ) or options, carefully consider your investment objectives, experience level, and risk tolerance. Over the counter leveraged Forex spot trading ( spot trading ) and options trading ( options trading ) both carry high levels of risk that may not be suitable for all investors. Educate yourself on the risks associated with spot and options trading, and seek advice from an independent fi nancial or tax advisor if you have any questions. With spot trading, you could lose some or all of your initial investment; do not invest money that you cannot afford to lose. Leverage, offered as part of spot trading, creates additional risk and loss exposure. With options trading, you could not only lose all of your initial investment, but the potential to lose money is potentially unlimited when you write an option. Purchasers and sellers of Forex options should familiarize themselves with the type of option (i.e., put or call) that they contemplate trading and the associated risks. You should calculate the extent to which the value of the options must increase for your position to become profi table, taking into account the premium paid, other transaction costs, if any, and rate of premium/time decay.
INTRODUCTION WELCOME TO FXDD S INTRODUCTION TO GREEKS OPTIONS GUIDE! As retail Forex continues to mature, FX traders are becoming more sophisticated. To meet the growing demand of these savvy traders who want more tools and flexibility, FXDD proudly offers FX Options. FX options are non-linear, multi-dimensional derivatives. You can trade FX options on FXDD s Options Trader platform. FXDD Options Trader comes equipped with the latest in options technology, including a built-in strategy optimizer, risk simulator, customizable interface, and Greek calculator. GREEKS ARE ESSENTIAL FOR DEFINING THE RISK OF YOUR INVESTMENTS. Each Greek calculation provides insights into different market factors that affect different aspects of a trade. MARKET FACTOR Underlying Spot Market Movement Underlying Spot Market Volatility Passage of Time Interest Rates OPTION PRICING RISK MEASUREMENT Delta and Gamma Vega Theta Psi and Rho OPTIONS EDUCATION 4
DELTA USE: Traders typically observe delta to get an edge in hedging or to see how in-the-money they are. EXPLANATION: Delta is a constantly changing number that measures how much an option s value changes as the underlying spot price changes. READING DELTA: Delta ranges from 0 to 1 for calls and 0 to -1 for puts and is often expressed as a percentage (0% to 100% for calls and 0% to -100% for puts). For Calls: When delta is at 0.5, the option is considered at-the-money. A higher number indicates that it s in-the-money, while a lower number indicates its out-of-the-money. For Puts: When delta is at -0.5, the option is considered at-the-money. A lower number indicates that it s in-the-money, while a higher number indicates its out-of-the-money. The delta is expressed as a curved line on a chart, as seen in the example below. 95.00 96.00 97.00 98.00 99.00 100.00 101.00 102.00 103.00 104.00 105.00 UNDERLYING SPOT MARKET PRICE The slope on the curve in the graph above becomes steeper at higher spot prices and flattens at lower spot prices. When the spot market price is: Close to the strike price the delta is approximately 0.50 Above the strike price the delta is greater than 0.50* Below the strike price the delta is less than 0.50* 0.4200 0.8500 0.8000 0.7500 0.7000 0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 *Under certain market scenarios, it is possible for slightly out-of-the-money FX calls to have a delta greater than 0.5. Similarly, under certain conditions, inthe-money calls can have a delta less than 0.5.* OPTIONS EDUCATION 5
DELTA AS HEDGE RATIO Delta can also be referred to as a hedge ratio as it expresses the number of the underlying currency necessary to create a hedged position at the current price only. For example, let s say we have a 101 call option with a delta of 0.42. If a position is composed of 100 of those calls, they would have a total delta of 42. For small changes in the spot market, those 100 calls would gain and lose money at the same rate as a position composed of 42 similar units of the spot market. Because delta is not a constant, as the spot market moves and time passes, the delta will change in value. This can cause a position of 100 calls hedged by 42 units of the underlying to become unhedged. DELTA IN ACTION In the following section, we will use an example to illustrate how you can read delta. All of the values are hypothetical, and have been applied to the delta formula. Consider the following market conditions for the cross rate ABC/XYZ. Underlying Spot Market Price: Underlying Spot Market Volatility: ABC (Base Currenct) Interest Rate: XYZ (Quote Currency) Interest Rate: 100.00 15.7% 3.00% 3.00% According to the option pricing formula (see our Appendix), a 101 call option with 30 days to expiration has, under these market conditions, a theoretical premium of 1.34 and a delta of 0.42 or 42%. The option price will change 42% as fast as the spot price. If the spot price increases 0.10, the option will gain about 0.04 (to 1.38); if the spot price decreases 0.10, the option will lose about 0.04 (to 1.30). OPTIONS EDUCATION 6
Here is a graph of the theoretical premium of this option with a current price of 1.34. 95.00 96.00 97.00 98.00 99.00 100.00 101.00 102.00 103.00 104.00 105.00 UNDERLYING SPOT MARKET PRICE Delta is the slope of the curve at current price. Here is the previous graph with a slope line added at the current spot price of 100.00. 1.34 0.00 4.50 4.25 4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 2.16 1.34 0.48 0.00 95.00 96.00 97.00 98.00 99.00 100.00 101.00 102.00 103.00 104.00 105.00 UNDERLYING SPOT MARKET PRICE 4.50 4.25 4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 The slope of the dashed line is (2.16 -.48) / (102.00 98.00) = 0.42. OPTIONS EDUCATION 7
GAMMA USE: Gamma measures how much an option s delta changes as the underlying spot price changes. EXPLANATION: Sometimes referred to as the option s curvature or the delta of the delta, gamma is expressed in deltas per unit of the underlying spot market. READING GAMMA: The number expressed by gamma is the change per point in the underlying spot market. For example, if gamma is equal to 0.075, this means that delta will change at a rate of 0.075 per point in the underlying spot market. GAMMA IN ACTION: In this section, we look at the same 101 30-day call option used in the delta section. The underlying spot market volatility was at 15.7%, the premium was 1.34, and the delta was 0.42. Its gamma is equal to 0.087. This means that the delta will change at a rate of 0.087 per point in the underlying spot market. More specifi cally, if the underlying spot market moves lower to 99, the option s delta will decrease 0.087 to 0.333 and if the underlying spot market moves higher to 101, the delta will increase 0.087 to 0.507. (Note that in the previous section it was shown that delta is close to 0.50 when the underlying spot market price is equal to the option s strike price.) OPTIONS EDUCATION 8
.507 0.4200.333 95.00 96.00 97.00 98.00 99.00 100.00 101.00 102.00 103.00 104.00 105.00 UNDERLYING SPOT MARKET PRICE At the current spot market price, the gamma = (0.507-0.333) / (101 99) = 0.087. 0.8500 0.8000 0.7500 0.7000 0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 Gamma will be greatest when the spot market and the strike price are equal; it will decrease as the option becomes very in-the-money or out-of-the-money. Like delta, gamma is not a constant either; it also changes as the underlying spot market changes and as time passes. Delta risk can be hedged by purchasing and/or selling quantities of the underlying market. A perfectly hedged position ( delta-neutral ) is not risk-free, however, since changes in the spot price can cause changes in the options deltas. Gamma provides information on how quickly this will occur. Gamma risk cannot be hedged with positions in the underlying market; it can only be offset with other option positions. OPTIONS EDUCATION 9
THETA Use: Under most market conditions, put and call options will lose value over time if the market does not change in price. For this reason, options are often called wasting assets. This loss of value over time is also referred to as time decay. Explanation: Theta measures how much an option s price will change over time; it is an indication of time decay, scaled to reflect the passage of one day. Volatility levels, moneyness (amount in- or out-of-the-money), days to expiration, and interest rates can all influence how time decay affects an option s price. Theta is usually not linear with time, i.e. a 60-day option will not lose 1/60th of its value every day. Sometimes time decay is faster than that; sometimes it is slower. For this reason, theta risk, like gamma risk, cannot be hedged with positions in the underlying spot market; it can only be controlled with other option positions. VEGA Vega measures how an option s value changes as market volatility changes. All options gain value as volatility increases. Like gamma and theta, vega risk cannot be controlled by trading spot market positions; it can only be offset by using other options. PSI AND RHO Psi and rho measure how an option s value changes as the interest rates for the base currency and the quote currency change. Although not to be ignored, changes in interest rates typically do not pose as great a risk to option traders as delta, gamma, theta, and vega risk. OPTIONS EDUCATION 10
APPENDIX The Garman-Kohlhagen option pricing model was developed by Mark B. Garman and Steven W. Kohlhagen in 1983 for pricing options on foreign exchange. It is an extension of the Black- Scholes option pricing formula. OPTIONS EDUCATION 11
CONTACT INFORMATION If you would like more information on FXDD and trading FX options, we would love to hear from you! LIVE CHAT: Talk to a Forex specialist in real time. https://secure.fxdd.com/mt/en/live-talk.html CALL US: +356.2013.3933 EMAIL US: sales@fxdd.com.mt OPTIONS EDUCATION 12
NOTES OPTIONS EDUCATION 13
NOTES OPTIONS EDUCATION 14
COPYRIGHT FXDD 2013