Derivative Engines - Options Handbook






Greeks:

Greeks are the quantities representing the sensitivities of the price of an option to a change in underlying parameters on which the value of the option is dependent.

All the parameters; spot price, volatility, interest rates, time to expiry changes by the life of the option. These changes on these parameters affect the option’s value, meaning that an option contract generates different positions on the spot price of the underlying asset, volatility of the underlying asset, interest rate of the underlying asset and a position against time.

In order to hedge an option or a portfolio of options all of these positions should be measured. Greeks are used to measure the different kind of risks that are taken by having an option position. Greeks are also called risk sensitivities, risk measures or hedge parameters.


Delta:

Delta measures the rate of change of the option value against the changes on the underlying asset’s value, which is the first derivative of the option against spot price. In other words defines the value of the spot position by having an option position. For example; if an investors holds an option contract of USD 1,000,000 notional and that option’s delta is % 25 then this investor has a long spot position of USD 250,000 on the underlying asset.


Gamma:

Gamma measures the rate of change of the option’s delta against the changes on the underlying asset’s value, which is the second derivative of the option against spot price. In other words defines how the spot position by having an option position is volatile. For example; if an investors holds an option contract of USD 1,000,000 notional and that option has a delta of USD 250,000 and a gamma of USD 50,000, then if spot moves % 1 above then delta of the option becomes USD 300,000.


Vega:

Vega measures the rate of change of the option value against the changes on the underlying asset’s volatility, which is the first derivative of the option against volatility. In other words defines the value of the volatility position by having an option position.


Theta:

Theta measures the rate of change of the option value against the changes on time to expiry, which is the first derivative of the option against time. In other words defines how much an option losses in one day if all the other parameters are fixed.


Rho:

Rho measures the rate of change of the option value against the changes in interest rates, which is the first derivative of the option against interest rates. In other words defines how much an option losses or gains if interest rates move % 1.


Derivative Engines is a Real Time option calculator. Please see the online option pricers below.

Options Structured Products
Vanilla Options Dual Currency Deposit
Multiple Options Portfolio Asymetric Forward
Knock In Barrier Options Zero Cost Collar
Knock Out Barrier Options Seagull (3 Way Collar)