This paper provides a discussion on the meaning and importance of Greeks in options trading. The following options are covered “Delta”, “theta”, “Gamma”, “Rho” and “Vega” which contribute to options pricing.
This submission is part of the Pre-Module Assignment for the Advanced Treasury Management – Financial Engineering module as part of MSC 25 course.
(B.) Main Body
Derivatives consisting of futures and options are trading instruments whose value is based on an underlying asset. The value of an option is the premium i.e. the price paid by the option buyer. The premium has 2 components (a) The Intrinsic Value = Difference between Strike Price and the Underlying ...view middle of the document...
The relationship can be thought of as an opportunity cost. In order to buy an option the buyer has to use funds from a deposit or borrow. Either way he incurs an interest rate cost. If interest rates go up then the opportunity costs of buying an option increases and to compensate the buyer the premium has to fall as otherwise the writer can earn a higher interest on the premiums. The situation is reversed when the interest rates fall. – Premiums will rise.
The volatility factor is a measure of the rate of fluctuation of market prices in the underlying instrument. Volatility measures price changes and does not take into account any direction. Historical volatility helps provide an estimate of future volatility whereas implied volatility is the proportional range, up or down within which the underlying instrument price is expected to finish at expiry. Generally higher volatility means greater the chance that the underlying price will move through the strike price and hence higher the premiums. Lower volatility means lesser the change it will hit the strike price and hence becoming profitable. Hence lower the premiums.
Because derivatives are tradable instruments they carry the same risks as any tradable instrument in the market. These include market, credit, operational and strategic risks. The most important risks associated with options pricing arise from the following.
Directional Risks – Resulting from price movements of the underlying
Time Risks – Resulting from time decay as the option reaches expiry
Volatility Risks – Resulting from the rate of change in the underlying.
As the above components are considered key factors in option pricing they need to be quantified so that they can be used in pricing models and one can assess the magnitude of their effects. Its important to understand how sensitive is the price of an option to any of the above risks. Each variable or sensitivity associated with the option pricing is identified using a Greek sounding letter; hence the term Option Greeks .The name is used because the most common of these sensitivities are often denoted by Greek letters. The following are the list of Greeks used to price the premium of an option.
Greek | Risk Associated with - | Value Equals |
Delta | Change in price of the underlying instrument | Change in PremiumChange in the price of the underlying |
Gamma | Change in Delta | Change in DeltaChange in the price of the underlying |
Vega | Change in the volatility of the underlying instrument price | Change in PremiumChange in the Volatility |
Theta | Change in the time to expiry | Change in PremiumChange in time to expiry |
Rho | Change in interest rates to fund the underlying instrument | Change in PremiumChange in time to expiry |
This is the measure of the sensitivity of the price of an option to a unit change in the price of the underlying.
Delta = Change in Premium...