# Valuation of Options

25/08/2020

The value of an option can be estimated using a variety of quantitative techniques based on the concept of risk neutral pricing and using stochastic calculus. In general, standard option valuation models depend on the following factors:

• The current market price of the underlying security
• The strike price of the option, particularly in relation to the current market price of the underlying asset (in the money vs. out of the money)
• The cost of holding a position in the underlying security, including interest and dividends
• The time to expiration together with any restrictions on when exercise may occur, and
• An estimate of the future volatility of the underlying security’s price over the life of the option.

#### The Valuation of Options

As we said before, options themselves have a value. Remember that options are totally separate entities to the underlying assets from which they are derived (hence, the term derivative). But in themselves they do have a value, which can be split into two parts: intrinsic value and time value.

In general:

• Intrinsic value is that part of the option’s value that is in-the-money (ITM).
• Time value is the remainder of the option’s value. Out-of-the-money (OTM) options will have no intrinsic value, and their price will solely be based on time value. Time value is another way of saying hope value. This hope is based on the amount of time left until expiration and the price of the underlying asset.
• A call is ITM when the underlying asset price is greater than the strike price.
• A call is OTM when the underlying asset price is less than the strike price.
• A call is at-the-money (ATM) when the underlying asset price is the same as the strike price.

Put options work the opposite way:

• A put is ITM when the underlying asset price is less than the strike price.
• A put is OTM when the underlying asset price is greater than the strike price.
• A put is ATM when the underlying asset price is the same as the strike price.