Black/Scholes Greeks
C denotes the Black/Scholes formula for the European call option and P denotes the
same thing for the European put option on a stock whose price is S .  , t , r , X denote the
volatility, time to maturity, interest rate, and strike price of the options, respectively. The
underlying stock will not pay a dividend for the period t to maturity. Changes in C with
respect to an infinitesimal change in  is denoted by the partial derivative
C
. Similarly

for the other parameters and for changes in P .
C
P
=
= S t N   d1  > 0, where N   x  is the standard normal density evaluated at


x.
S N   d1 
C
=
+ Xre  rt N  d2  > 0,
t
2 t
P
C
=
- Xre  rt > 0 if the put is near or out of the money
t
t
< 0 if the put is deep in the money.
C
P
= e rt N  d2  < 0 <
= e rt N  d2 
X
X
C
P
= N  d1  > 0 >
= N  d1  - 1.
S
S
C
P
C
= Xte rt N  d2  > 0 >
=
- Xte  rt .
r
r
r