  Greeks Explained

1) Greeks Definition

The ‘greeks’ is the term used to describe attributes of a derivatives trade that are commonly represented by Greek letters, such as delta, vega, and gamma.  The term is typically lowercase because it describes a group of letters… whereas ‘Greeks’ would refer to people from Greece.

The term attributes as mentioned above refers to either:

a) The change in the MTM of a derivative trade caused by changes in the inputs that are used to value that trade.  These are called ‘first order’ greeks (a.k.a., first order sensitivities).

b) The changes in one of the first order greeks to changes in the inputs that are used to value a derivative.   These are called ‘second order’ greeks (a.k.a., first order sensitivities).

The inputs that are used to value a derivative can be one or more of the following:

a) Market prices, e.g., commodity prices such as the market price of crude oil

b) Volatility, i.e., how much the price of something changes over time.  Big moves up and/or down means a larger volatility number.

c) Interest Rates

d) Time, i.e., the time between the current day and the expiration date of an option

e) Correlations, i.e., how two items move in conjunction with one another

2) List of the greeks

This is a list of the most commonly used greeks:

 # Name Input Order Description 1 Delta Prices First Order Change in MTM of a derivative trade due to changes in market prices 2 Gamma Prices Second Order Change to the Delta due to changes in market prices 3 Vega Volatility First Order Change in MTM of a derivative trade due to changes in volatilities 4 Vega-Gamma Volatility Second Order Change to the Vega of a derivative trade due to changes in volatilities 5 Theta Time First Order Change in MTM of a derivative trade due to changes in time 6 Rho Interest Rate First Order Change in MTM of a derivative trade due to changes in interest rates 7 Correlation Vega Correlations First Order Change in MTM of a derivative trade due to changes in correlations 8 Correlation Vega-Gamma Correlations Second Order Change to the Correlation Vega of a derivative trade due to changes in volatilities

3) Delta

With regards to commodity derivatives, there are four versions or interpretations of the greek known as ‘delta’.

A) Delta as unitless number… ranges from -1 to 1.

B) Delta in currency.  Ranges from -infinity to + infinity

Interpretation: How much \$\$\$ you make for a one tick move.  One tick is sometimes called the 'delta shift' and could be \$0.01, \$0.001 or other.

E.g., if Delta shift is \$0.01 (one penny) and your delta is \$12… then you make \$12 if the market goes up by \$0.01.

C) Delta in units

This is your delta in BBL (barrels) or MT (metric tons) or whatever the unit of your commodity option.

E.g., if you are long 10000BBL Crude Oil option and it is at the money… your unitless delta may be around 0.50 and your delta in units would be 5000BBL (i.e., 0.50 * 10000BBL).

D) Delta in contracts

This is the delta expressed in units… and then that number divided by the contract size.    The contract size refers to the standard traded size of trades as done on commodities exchanges.  E.g., for crude oil the typical contract size is 1 Contract = 1000 BBL

So, for example, if your delta in units for crude oil is 10,000 BBL… then your delta in contracts is:

10,000BBL * 1 Contract / 1000 BBL = Delta in Contracts of 10

4) Delta as Position, Long or Short vs. Buy or Sell

The term ‘Delta’ is often used as a generic term for position, meaning if you are long or short a commodity.  Long means that you make money if the price of a commodity rises and short means you make money if the price of a commodity goes down.

With options there are two flavors, calls and puts.  With calls you tend to make money if the market goes up when you buy the call.  With puts you tend to make money if the market goes down if you buy the puts.

This chart summarizes the variations

 # Put/Call Buy/Sell Long/Short Want the market to go… 1 Put Buy Short Down 2 Put Sell Long Up 3 Call Buy Long Up 4 Call Sell Short Down

5) Delta By Time Period

Normally for delta position reports for commodities or interest rates, you would want to see your delta at different time periods.  For example if you are long 100 contract equivalents of June 2014 crude oil and short 100 contract equivalents of August 2014 crude oil… if you didn’t look at the time, you would report your position as 0.000 (zero).  However, you still have risk because the price of June crude oil can move independently of the price of December crude oil.   So a typical delta position report would show your positions something like this:

Month                 Delta in Contracts

Jun  2014              +100

Jul 2014                   0

Aug 2014               -100

Total                        0

6) Delta Weightings

The price of commodities is more volatility for months near the current month than for months farther out in the future.

For example, suppose the price of crude oil for delivery in two months is \$80 and the price of crude oil for delivery 48 months from now is also \$80.

Time                     Price

2 months          \$80/BBL

48 months        \$80/BBL

Now suppose there is some unplanned event such as a hurricane that impacts the price of crude oil.  What might happen?  The price in the short term might spike due to supply interruption.  On the other hand, we would expect that within a short period the supply would be restored as hurricane damage is repaired.   For example, the prices might spike \$5 in the short term and perhaps farther out in time the effect is only \$1.

So you get this:

Time                     Price         Change

2 months          \$85/BBL      \$5/BBL

48 months        \$81/BBL      \$1/BBL

The above is just an example to illustrate the point that commodity prices for delivery in the short term tend to be more volatile, i.e., experience bigger percentage moves than for commodity prices for farther out in the future (i.e., the long term).

So suppose you were long 10,000 BBL of crude for delivery in the short term at 2 months out and short 10,000 BBL for delivery in the longer term at 48 months.  You might think you position is overall flat because it net out to zero.  However, because the prices in the short term are more volatility, a \$1 move in the price of 2-month out crude oil may only change the price of 48-month crude oil by 50% (note that the 50% value is just an example).

So if you want to sum the delta positions from different months, it may make sense to multiply each of the future months by a percent that reflects how the future month varies with relation to the first month.

E.g., you might have ratios like this

Month       Ratio

1 month     100%

2 months    98%

24 months  70%

….

48 months 50%

So using those ratios and our position examples:

 Month Ratio Unweighted Delta Weighted Delta 2 98% 10,000 BBL 9,800 BBL 48 50% -10,000 BBL -5,000 BBL Total 0 BBL 4,800 BBL

So if you use an unweighted delta then you’ll show your overall position as flat (though you would still be long one month vs. short another).  On the other hand, if you look at the total weighted delta number of 4,800 your consider yourself long the market.    The weighted delta may be more accurate in terms of what would actually happen if a shock causes market prices to move up or down.