It is important for option traders to understand the complexity surrounding options. Knowing the anatomy of options allows traders to use sound judgment and gives them more options to execute trades.

## The Greeks

The value of an option has several elements that go hand in hand with the “Greeks”:

- The price of the underlying security
- Expiry time
- Implied volatility
- The actual strike price
- Dividends
- Interest rates

The “Greeks” provide important information on risk management, helping to rebalance portfolios to achieve desired exposure (eg delta hedging). Each Greek measures how the portfolio reacts to minor changes in a particular underlying factor, allowing individual risks to be examined.

*Delta* measures the rate of change in the value of an option in relation to changes in the price of the underlying asset.

Spectrum* *measures the rate of change in the delta in relation to changes in the price of the underlying asset.

Lambda, or elasticity, relates to the percentage change in the value of an option compared to the percentage change in the price of the underlying asset. This offers a means of calculating leverage, which can also be called leverage.

Theta calculates the sensitivity of the option’s value over time, a factor known as “time decay.”

Vega measures susceptibility to volatility. Vega is the measure of the value of the option with respect to the volatility of the underlying asset.

Rho assesses the reactivity of the value of the option to the interest rate: it is the measure of the value of the option with respect to the risk-free interest rate.

Therefore, using the Black Scholes model (considered the standard model for pricing options), the Greeks are reasonably simple to determine and are very useful for day traders and derivatives traders. To measure time, price and volatility, delta, theta and vega are effective tools.

The value of an option is directly affected by “time to expiration” and “volatility”, where:

- A longer period of time before expiration tends to increase the value of call and put options. The reverse of this is also the case, as a shorter period of time before expiration can create a drop in the value of call and put options.
- Where there is higher volatility, there is an increase in the value of call and put options, while lower volatility leads to a decrease in the value of call and put options.

The price of the underlying security has a different effect on the value of call options compared to put options.

- Typically, as the price of a security increases, the corresponding direct call options follow this increase by gaining value, while the put options fall in value.
- When the security price falls, the opposite occurs, and direct call options generally experience a decrease in value, while put options increase in value.

## A premium of options

This occurs when a trader buys an options contract and pays an amount in advance to the seller of the options contract. This option premium will vary, depending on when it was calculated and in which option market it is purchased. The premium may even differ within the same market, based on the following criteria:

- Is the option in, in or out of the money? An in-the-money option will sell at a higher premium, as the contract is already profitable and the buyer of the contract can access this profit immediately. In contrast, cash or no-money options can be purchased for a lower premium.
- What is the time value of the contract? Once an option contract expires, it ceases to have value, so it is logical to think that the longer the term until the expiration date, the higher the premium. This is because the contract contains additional time value, as there is more time in which the option can become profitable.
- What is the level of market volatility? The premium will be higher if the options market is more volatile, as there is a greater chance of getting higher profits from the option. The reverse also applies: lower volatility means lower premiums. The volatility of an options market is determined by applying various price ranges (long-term, recent, and expected price ranges are the required data) to a selection of volatility pricing models.

Call and put options do not have matching values when they reach their mutual ITM, ATM and OTM strike prices due to direct and opposite effects where they oscillate between uneven distribution curves (example below), thus becoming unequal .

Strikes are the number of strikes and the increments between strikes are decided by the exchange in which the product is traded.

## Option pricing models

When using historical volatility and implied volatility for business purposes, it is important to consider the differences involved:

Historical volatility calculates the rate at which the underlying asset has been experiencing movement during a specific period of time, where the annual standard deviation of price changes is given as a percentage. Measures the degree of volatility of the underlying asset during a specific number of previous trading days (modifiable period), before each calculation date in the information series, for the selected period of time.

Implied volatility is the combined future estimate of the underlying asset’s trading volume, providing an indicator of how the asset’s daily standard deviation can be expected to vary between the time of calculation and the option’s expiration date. When analyzing the value of an option, implied volatility is one of the key factors a day trader should consider. When calculating implied volatility, an option pricing model is used, taking into account the cost of an option’s premium.

There are three frequently used theoretical pricing models that daily traders can use to help calculate implied volatility. These models are the Black-Scholes, Bjerksund-Stensland and Binomial models. The calculation is done with the use of algorithms, generally using call and put options at-the-money or closer to the money.

- The Black-Scholes model is most commonly used for European-style options (these options can only be exercised on the expiration date).
- The Bjerksund-Stensland model effectively applies to American-style options, which can be exercised at any time between the purchase of the contract and the expiration date.
- The Binomial model is appropriately used for American, European and Bermudan style options. Bermudan is a style halfway between a European and American style option. The Bermudan option can be exercised only on specific days during the contract or on the expiration date.