When finance people talk about "The Greeks" they don't mean the lunchcounter on Amsterdam
Ave! "The Greeks" in this context refer to the changes in the price of an option when some of
the parameters are changed.
So what?
Consider an example about employee stock options, which can teach you something that your
employer doesn't want you to know! Suppose you were granted a stock option long ago,
exercising when the stock is $35 but now the company stock is $70. Should you cash in the
option now? Your colleagues tell you to wait, the company is about to release some new
products, things are going really good, that the latest investment report had a target of $80 per
share. If you cash out now, you get $35; if you wait you could get $45 or who knows how much
more!?!!
This is a realistic depiction: many tech companies have huge "overhangs" of stock options
granted to employees long ago, that their employees are just waiting to cash in. But wait
is
this really smart?
What is the stock option worth today? Well, if you cashed it in you would get $35. There is not
really any probability to worry about
the probability that the stock could fall that far is, by
any conventional measure (assuming volatility and returns are not too crazy), almost zero. So in
the Black-Scholes formula, the d
1
and d
2
terms are .9999 or more and the option is worth its
intrinsic value. So if you exercised the option, you could put $35 of your own money together
with the option and buy one share of the company's stock.
So how would your portfolio (of one share of stock) compare against one of your co-workers,
who has an option with an exercise price of $35 just like you had? Well, if the company's stock
goes up by $1 then her option is worth $1 more; just like your stock share is worth $1 more. If
the company's stock goes up $10 then her option is worth $10 more, just like yours is. It doesn't
matter whether you cash out or not, your wealth is the same.
(Apart from things like tax considerations, of course
I'm not giving any practical real-world advice since I'm not your accountant!)
When the stock price gets so high above the exercise price, the call price approaches its intrinsic
value (we did this several chapters before). Another way of putting it, the change in the call
price,
, is approximately the same as the change in the stock price that underlies the
option,
. Or we could write that, for very high S, the ratio,
, is approaching
one. This ratio,
, is called
. We used
back in Chapter 11 to construct trees (and
warned you that
would be back, like a cheesy horror movie villain who keeps rising from the
dead to attack again!).