Forex Walkthrough
Trading  Options
Delta, gamma, and volatility are concepts familiar to nearly all options traders. However, these same tools used to trade currency options can also be useful in predicting movements in the underlying spot price in the forex market. In this section, we look at how volatility can be used to determine upcoming market activity, how delta can be used to calculate the probability of spot movements, and how gamma can predict trading environments.
Using Volatility to Forecast Market Activity
Option volatility information is widely available. In using volatility to forecast market activity, the trader needs to make certain comparisons. The most reliable comparison is implied versus actual volatility, but the availability of actual data is limited. Alternatively, comparing historical implied volatilities are also effective. Onemonth and threemonth implied volatilities are two of the most commonly benchmarked time frames used for comparison (the numbers below represent percentages).
Here is what the comparisons indicate:
Breakout traders, on the other hand, can also monitor option volatilities to make sure that they are not buying or selling into a false breakout. If volatility is at average levels, the probability of a false breakout increases. Alternatively, if volatility is very low, the probability of a real breakout increases. These guidelines typically work well, but traders also have to be careful. Volatilities can have long downward trends (as they did between June and October 2002) during which time volatilities can be misleading and misinterpreted. Traders need to look for sudden sharp movements in volatilities, not gradual ones.
The following is a chart of USD/JPY currency pair. The green line represents shortterm volatility, the red line represents longterm volatility and the blue is line price action. The arrows with no labels are pointing to periods when shortterm volatility rises significantly above longterm volatility. You can see such divergence in volatility tends to be followed by periods of range trading. The "1M implied" arrow is pointing to a period when shortterm volatility dips below longterm volatility. At price action above that, a breakout occurs when shortterm volatility reverts back toward longterm volatility.
Using Delta to Calculate Spot Probabilities
What Is Delta?
Options price can be seen as a representation of the market's expectation of the future distribution of spot prices. The delta of an option can be thought of roughly as the probability that the option will finish in the money. For example, given a onemonth USD/JPY call option struck at 104 with a delta of 50, the probability of USD/JPY finishing above 104 one month from now would be approximately 50%.
Calculating Spot Probabilities
With information on deltas, one can approximate the market's expectation of the likelihood of different spot levels over time. When it is likely that the spot will finish above a certain level, calloption deltas are used. Similarly, when the spot is likely to finish below a certain level, putoption deltas are used.
We will be using conditional probability to calculate expected spot values. Given two events, A and B, the probability of event A and B occurring is calculated as follows:
In other words, the probability of A and B occurring is equal to the probability of A times the probability of B given that A has occurred. Applying this formula to the problem of calculating the probability that spot will touch a certain level, we get:
In other words, the probability of spot touching and finishing above a certain level (or delta) is equal to the probability of the spot touching that level multiplied by the probability of the spot finishing above a certain level given that is has already touched that level.
Given options prices and their corresponding deltas, this probability calculation can be used to get a general sense of the market's expectations of various spot levels. The rule of thumb this methodology yields is that the probability of spot touching a certain level is roughly equivalent to two times the delta of an option struck at that level.
Using Gamma to Predict Trading Environments
What Is Gamma?
Gamma represents the change in delta for a given change in the spot rate. In trading terms, players become long gamma when they buy standard puts or calls, and short gamma when they sell them. When market commentators speak of the entire market being long or short gamma, they are usually referring to market makers in the interbank market.
How Market Makers View Gamma
Generally, options market makers look to be delta neutral  that is, they want to hedge their portfolios against changes in the underlying spot rate. The amount by which their delta, or hedge ratio, changes is known as gamma.
If, for example, a trader is long gamma, this means he or she has bought some standard vanilla options. Assume they are USD/JPY options and that the delta position of these options is $10 million at USD/JPY 107; in this case, the trader will need to sell $10 million USD/JPY at 107 in order to be fully insulated against spot movement.
If USD/JPY rises to 108, the trader will need to sell another $10 million, this time at 108, as the total delta position becomes $20 million. What happens if USD/JPY goes back to 107? The delta position goes back to $10 million, as before. Because the trader is now short $20 million, he or she will need to buy back $10 million at 107. The net effect then is a 100pip profit, selling a 108 and buying at 107.
In sum, when traders are long gamma, they are continually buying low and selling high, or vice versa, in order to hedge. When the spot market is very volatile, traders earn a lot of profits through their hedging activity. But these profits are not free, as there is a premium to own the options. In theory, the amount you make from delta hedging should exactly offset the premium, but in practice this depends on the actual volatility of the spot rate.
The reverse is true when a trader has sold options. When short gamma, in order to hedge the trader must continually buy high and sell low. As such, he or she loses money on the hedges. In theory, it's the exact same amount earned in options premium through the sales.
Why Is Gamma Important for Spot Traders?
But what relevance does all this have for regular spot traders? The answer is that spot movement is increasingly driven by the activity in the options market. When the market is long gamma, market makers as a whole will be buying spot when the exchange rate falls and selling spot when it rises. This behavior can generally keep the spot rate in a relatively tight range.
When the market is short gamma, however, the spot rate can be prone to wide swings as players are either continually selling when prices fall, or buying when prices rise. A market that is short gamma will exacerbate price movement through its hedging activity. Thus:
There are many tools used by seasoned options traders that can also be useful to trading spot FX. Volatility can be used to forecast market activity in the cash component through comparing shortterm versus longer term implied volatilities. Delta can help estimate the probability of the spot rate reaching a certain level. And gamma can predict whether spot will trade in a tighter range if it is vulnerable to wider swings.
Using Volatility to Forecast Market Activity
Option volatility information is widely available. In using volatility to forecast market activity, the trader needs to make certain comparisons. The most reliable comparison is implied versus actual volatility, but the availability of actual data is limited. Alternatively, comparing historical implied volatilities are also effective. Onemonth and threemonth implied volatilities are two of the most commonly benchmarked time frames used for comparison (the numbers below represent percentages).
Source: IFR Market News Plugin 
Here is what the comparisons indicate:
 If shortterm option volatilities are significantly lower than longterm volatilities, expect a potential breakout.
 If shortterm option volatilities are significantly higher than longterm volatilities, expect reversion to range trading.
Breakout traders, on the other hand, can also monitor option volatilities to make sure that they are not buying or selling into a false breakout. If volatility is at average levels, the probability of a false breakout increases. Alternatively, if volatility is very low, the probability of a real breakout increases. These guidelines typically work well, but traders also have to be careful. Volatilities can have long downward trends (as they did between June and October 2002) during which time volatilities can be misleading and misinterpreted. Traders need to look for sudden sharp movements in volatilities, not gradual ones.
The following is a chart of USD/JPY currency pair. The green line represents shortterm volatility, the red line represents longterm volatility and the blue is line price action. The arrows with no labels are pointing to periods when shortterm volatility rises significantly above longterm volatility. You can see such divergence in volatility tends to be followed by periods of range trading. The "1M implied" arrow is pointing to a period when shortterm volatility dips below longterm volatility. At price action above that, a breakout occurs when shortterm volatility reverts back toward longterm volatility.

Source: Figure 1 
What Is Delta?
Options price can be seen as a representation of the market's expectation of the future distribution of spot prices. The delta of an option can be thought of roughly as the probability that the option will finish in the money. For example, given a onemonth USD/JPY call option struck at 104 with a delta of 50, the probability of USD/JPY finishing above 104 one month from now would be approximately 50%.
Calculating Spot Probabilities
With information on deltas, one can approximate the market's expectation of the likelihood of different spot levels over time. When it is likely that the spot will finish above a certain level, calloption deltas are used. Similarly, when the spot is likely to finish below a certain level, putoption deltas are used.
We will be using conditional probability to calculate expected spot values. Given two events, A and B, the probability of event A and B occurring is calculated as follows:
P(A and B) = P(A)*P(BA) 
In other words, the probability of A and B occurring is equal to the probability of A times the probability of B given that A has occurred. Applying this formula to the problem of calculating the probability that spot will touch a certain level, we get:
P(touching and finishing above spot level) = P(touching spot level) * P(finishing above spot  touched spot level) 
In other words, the probability of spot touching and finishing above a certain level (or delta) is equal to the probability of the spot touching that level multiplied by the probability of the spot finishing above a certain level given that is has already touched that level.
Example Suppose that we want to know the probability that the EUR/USD will touch 1.26 in the next two weeks. Because we are interested in spot finishing above this level, we look at the EUR call option. Given current spot and volatilities, the delta of this option is 30. Therefore, the market\'s view is that the odds of EUR/USD finishing above 1.26 in two weeks are roughly 30%. If we assume that EUR/USD does touch 1.26, the option delta then would become 50. By definition an atthemoney option has a delta of 50, and thus has a 1/2 chance of finishing in the money. Here is the calculation using the above equation: 0.3 = P(touching 1.26) * 0.5 This means the odds of EUR/USD touching 1.26 in two weeks equals 60% (0.3/ 0.5). The market\'s "best guess" then is that EUR/USD has a 60% chance of touching 1.26 in two weeks, given the information from options. 
Using Gamma to Predict Trading Environments
What Is Gamma?
Gamma represents the change in delta for a given change in the spot rate. In trading terms, players become long gamma when they buy standard puts or calls, and short gamma when they sell them. When market commentators speak of the entire market being long or short gamma, they are usually referring to market makers in the interbank market.
How Market Makers View Gamma
Generally, options market makers look to be delta neutral  that is, they want to hedge their portfolios against changes in the underlying spot rate. The amount by which their delta, or hedge ratio, changes is known as gamma.
If, for example, a trader is long gamma, this means he or she has bought some standard vanilla options. Assume they are USD/JPY options and that the delta position of these options is $10 million at USD/JPY 107; in this case, the trader will need to sell $10 million USD/JPY at 107 in order to be fully insulated against spot movement.
If USD/JPY rises to 108, the trader will need to sell another $10 million, this time at 108, as the total delta position becomes $20 million. What happens if USD/JPY goes back to 107? The delta position goes back to $10 million, as before. Because the trader is now short $20 million, he or she will need to buy back $10 million at 107. The net effect then is a 100pip profit, selling a 108 and buying at 107.
In sum, when traders are long gamma, they are continually buying low and selling high, or vice versa, in order to hedge. When the spot market is very volatile, traders earn a lot of profits through their hedging activity. But these profits are not free, as there is a premium to own the options. In theory, the amount you make from delta hedging should exactly offset the premium, but in practice this depends on the actual volatility of the spot rate.
The reverse is true when a trader has sold options. When short gamma, in order to hedge the trader must continually buy high and sell low. As such, he or she loses money on the hedges. In theory, it's the exact same amount earned in options premium through the sales.
Why Is Gamma Important for Spot Traders?
But what relevance does all this have for regular spot traders? The answer is that spot movement is increasingly driven by the activity in the options market. When the market is long gamma, market makers as a whole will be buying spot when the exchange rate falls and selling spot when it rises. This behavior can generally keep the spot rate in a relatively tight range.
When the market is short gamma, however, the spot rate can be prone to wide swings as players are either continually selling when prices fall, or buying when prices rise. A market that is short gamma will exacerbate price movement through its hedging activity. Thus:

When market makers are long gamma, spot generally trades in a tighter range.

When market makers are short gamma, spot can be prone to wide swings.
There are many tools used by seasoned options traders that can also be useful to trading spot FX. Volatility can be used to forecast market activity in the cash component through comparing shortterm versus longer term implied volatilities. Delta can help estimate the probability of the spot rate reaching a certain level. And gamma can predict whether spot will trade in a tighter range if it is vulnerable to wider swings.
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