Page 164 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Unit 12: Risk Management with Derivatives I

12.1 Hedging using Greeks (Delta-Gamma Hedging) Notes

The sensitivity analysis of option premium deals with the measurement of changes in option
price due to the change in the underlying parameters that determine the option prices. These
parameters include stock price, time period, interest rate and volatility. As the price of the
underlying asset rises or falls, options are more or less likely to finish in-the-money and their
values rise or fall accordingly. As volatility rises, the extreme outcomes are more likely to
increase an option's value. As volatility falls or as expiration date approaches, the extreme
outcomes are less likely to occur and the option value decreases.
There are five sensitivity measures. They are:
1. Delta

2. Gamma
3. Theta
4. Rho

5. Vega
12.1.1 Delta of an Option

Delta is a measure of the sensitivity the calculated option value has to small changes in the share
price. The delta of an option tells you by how much the premium of the option would increase
or decrease for a unit change in the price of the underlying. This can help the buyer of an option
as to which call/put option should be bought.
Delta is positive for a bullish position (long call and short put) as the value of the position
increases with rise in the price of the underlying. Delta is negative for a bearish position (short
call and long put) as the value of the position decreases with rise in the price of the underlying.

!
Caution Delta varies from 0 to 1 for call options and from –1 to 0 for put options. Some
people refer to delta as 0 to 100 numbers.

Symbolically, option delta is given as N (d ).
1
Example: An option with delta of 0.4, the premium of the option would change by 40
paise for a Re 1 change in the price of the underlying. Delta is about 0.4 for near/at the money
options. As the option becomes in the money, the value of delta increases. Conversely as the
option becomes out of the money, the value of delta decreases.

12.1.2 Option Gamma

Gamma is a measure of the calculated delta's sensitivity to small changes in share price. The
gamma of an option tells you how much the delta of an option would increase or decrease for a
unit change in the price of the underlying.
If we were to explain in very simple terms: if delta is velocity, then gamma is acceleration. Delta
tells you how much the premium would change; gamma changes delta and tells you how much
the next premium change would be for a unit price change in the price of the underlying.
Gamma is positive for long positions (long call and long put) and negative for short positions
(short call and short put). Gamma does not matter much for options with long maturity. However

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