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Greeks Explained
Also
see Option Pricing Models
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
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 |
|
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.