36 lines
2.6 KiB
Plaintext
36 lines
2.6 KiB
Plaintext
848 Part VI: Measuring and Trading Volatmty
|
||
THE "GREEKS"
|
||
Risk measurements have generally been given the names of actual or contrived
|
||
Greek letters. For example, "delta" was discussed in previous chapters. It has become
|
||
common practice to refer to the exposure of an option position merely by describing
|
||
it in terms of this "Greek" nomenclature. For example, "delta long 200 shares" means
|
||
that the entire option position behaves as if the strategist were merely long 200 shares
|
||
of the underlying stock. In all, there are six components, but only four are heavily
|
||
used.
|
||
DELTA
|
||
The first risk measurement that concerns the option strategist is how much current
|
||
exposure his option position has as the underlying security moves. This is called the
|
||
"delta." In fact, the term delta is commonly used in at least two different contexts: to
|
||
express the amount by which an option changes for a I-point move in the underlying
|
||
security, or to describe the equivalent stock position of an entire option portfolio.
|
||
Reviewing the definition of the delta of an individual option (first described in
|
||
Chapter 3), recall that the delta is a number that ranges between 0.0 and 1.0 for calls,
|
||
and between -1.0 and 0.0 for puts. It is the amount by which the option will move if
|
||
the underlying stock moves 1 point; stated another way, it is the percentage of any
|
||
stock price change that will be reflected in the change of price of the option.
|
||
Example: Assume an XYZ January 50 call has a delta of 0.50 with XYZ at a price of
|
||
49. This means that the call will move 50% as fast as the stock will move. So, if XYZ
|
||
jumps to 51, a gain of 2 points, then the January 50 call can be expected to increase
|
||
in price by 1 point (50% of the stock increase).
|
||
In another context, the delta of a call is often thought of as the probability of the
|
||
call being in-the-money at expiration. That is, ifXYZ is 50 and the January 55 call has
|
||
a delta of 0.40, then there is a 40% probability that XYZ will be over 55 at January
|
||
expiration.
|
||
Put deltas are expressed as negative numbers to indicate that put prices move
|
||
in the opposite direction from the underlying security. Recall that deltas of out-of
|
||
the-money options are smaller numbers, tending toward 0 as the option becomes
|
||
very far out-of-the-money. Conversely, deeply in-the-money calls have deltas
|
||
approaching 1.0, while deeply in-the-money puts have deltas approaching -1.0.
|
||
Note: Mathematically, the delta of an option is the partial derivative of the
|
||
Black-Scholes equation ( or whatever formula one is using) with respect to stock
|
||
price. Graphically, it is the slope of a line that is tangent to the option pricing curve. |