1. Derivatives
Lecture 21

2. Greeks Delta Gamma Theta Vega Rho
The Greeks measure the various risks of an option.
Every option has risk related to the variables contained in the price of the option.
Knowing these risks allows us to create strategies and select the best option to include in the strategy.

3. Greeks
Delta - D
the rate of price change for an option, relative to the price change in the underlying asset
Also called the Hedge Ratio
D = N(d1) = DC / DP

4. Greeks
Gamma -G
The rate of change in delta, relative to the price change of the asset
G = N(d1)p - N(d1)p+1

5. Greeks
Theta - Q
The rate of change in the option price relative to a one day change in expiration
Also called Time Decay
Q = Ct - Ct-1

6. Greeks
Vega - L
The rate of change in the option price relative to a 1% change in the volatility
L = Cv - Cv+.01

7. Greeks
Rho
The rate of change in the option price relative to a 1% increase in the discount rate
Rho = Cr - Cr+.01

8. Greeks Example - original data Call = 1.70 r = 10%
Stock = 36 time = 90/365 days
Strike = 40 volatility = .40
Delta = N(d1) = .3794
Gamma = N(d1)p - N(d1)p+1
= =

9. Greeks = 1.695-1.725 = .0300 example - continued Theta = Ct - Ct-1 =
= = (daily)
= x 260 = (annual)
Vega = Cv - Cv+.01
= =
Rho = = Cr - Cr+.01 (using NUMA Web Option Calculator)
= = .0300