## Table of contents

## Overview

If you are already an options trader or an aspiring options trader then you will need to know how to price an option. Or at least the calculations and methods used to price options.

There are many tools available online to assist with options pricing. Many of these tools also calculate implied volatility and the option Greeks.

## Black Scholes Model

Options pricing used to be a black art with no way to determine the true value of options. In 1973, Fischer Black and Myron Scholes published their ground breaking work in an article entitled “The Pricing of Options and Corporate Liabilities”. Robert Merton and Myron Scholes were awarded the Nobel Memorial Prize in Economic Sciences in 1997. Fischer Black died in 1995 but was recognised by the Swedish academy.

This work became known as the Black Scholes options pricing model.

The Black Scholes model allows the calculation of a theoretical estimate of the price for European style options.

Options trading exploded globally after the publication of the Black Scholes model. From that point traders and investors were able to calculate the true value of options.

## In The Money Options

An in the money option is one that has intrinsic value as well as extrinsic value.

If XYZ stock is trading at £10 per share, then an XYZ call option with a strike price of £9.50 is an in the money option. Similarly an XYZ put option with a strike price of £10.50 is also an in the money option.

Both of these options have an intrinsic value of £0.50.

They will also have extrinsic value. This will depend on other factors such as implied volatility, time to maturity, risk free rate.

## Out Of The Money Options

An out of the money option is one that has no intrinsic value and some extrinsic value.

If XYZ stock is trading at £10 per share, then an XYZ call option with a strike price of £10.50 is an out of the money option. Similarly an XYZ put option with a strike price of £9.50 is also an in the money option.

Both of these options have no intrinsic value.

They will have some extrinsic value. Just like in the money options the amount will depend on other factors.

## At The Money Options

You can probably guess that an at the money option occurs when the underlying asset is trading at the same level as the strike price.

These types of options have no intrinsic value but do have extrinsic value.

## Options Premium

The option premium is the current market price of an option contract. When an option writer sells an options contract they receive the option premium as income.

The options premium for in the money options are comprised of intrinsic and extrinsic value.

The options premium for out of the money options is purely the extrinsic value.

## Implied Volatility

Implied volatility is a statistic that calculates the likelihood of a future change in a given asset price. Traders can use implied volatility data to determine whether a price target is feasible within a given time frame.

Implied volatility has a major effect on the price of options. An asset with a high implied volatility will have a higher option premium than an asset with a low implied volatility. Supply and demand, along with time value, are major factors for calculating implied volatility. Implied volatility tends to increase in bear markets and decrease in bull markets.

Implied volatility is not the same as historical volatility. Historical volatility measures past market changes.

## What Are Option Greeks?

Many options traders will make reference to obscure symbols or terminology. These are often referred to as trading Greeks or option Greeks. This is because they relate to Greek symbols.

All option Greeks are used to specify an element of risk within options trading. The following sections identify some of the more common option Greeks.

### Delta

Delta (Δ) represents the rate of change between the option price and a £1 change in the underlying asset price.

Example.

The “XYZ December 850 call” option has a delta of 0.50. This means for every £1 increase in the XYZ share price the option price should also increase by £0.50.

A trader can also use the delta to determine how many options contracts they need to write to create a covered option position.

### Theta

Theta (Θ) represents the rate of change between the option price and time. This is often referred to as time decay. If all other factors are equal then theta indicates how much an option price decreases as the time to expiration decreases.

Theta is highest for at the money options. Theta also accelerates as the expiration date approaches.

Option buyers will usually have a negative theta.

Option writers will usually have a positive theta.

Example.

A trader owns a “XYZ December 850 call” option with a theta of -0.50. The option price would decrease by £0.50 for every day that passes

### Gamma

The term gamma (Γ) is where options pricing starts to get really involved. The gamma refers to how much the delta (Δ) changes for a £1 change in the underlying asset.

Example.

A trader owns a “XYZ December 850 call” option. This call option has a delta of 0.50 and a gamma of 0.20. If XYZ stock increases or decreases by £1 then the delta would increase or decrease by 0.20.

The gamma therefore determines how sensitive the delta is to changes in the price of the underlying asset. A high gamma would indicate that the option price is susceptible to large fluctuations.

### Vega

The term vega (v) represents the rate of change between an option price and the implied volatility. Vega is therefore how sensitive an option price is to changes in volatility. Vega is the amount an option price changes for a 1% change in implied volatility.

Example.

An option has a vega of 0.10. The option price is expected to change by £0.10 for each 1% change in implied volatility.

### Rho

The term rho (p) represents the rate of change between an option price and a 1% change in the risk free rate. Rho is therefore how sensitive an option price is to changes in the risk free rate of interest.

Example.

An option has a rho of 0.25 and a price of £2.50. If the risk free rate of interest rises by 1% then the option price would increase to £2.75.