Following up on my article titled “Beginners guide on options contracts,” the premium is the price that the buyer of an option pays to buy an options contract and the money that an option seller (writer) pays to sell an options contract. The ‘pricing’ term on the title of this article refers to this premium amount.

The premium price of an options contract derives from three key factors, the intrinsic value, the time value, and the volatility factor.

The intrinsic value is the difference between the price of the underline asset and the option contract strike price. When, for example, the strike price of a call options contract is $50 and the actual price of the underline asset is $55, then the intrinsic value of the options contract is $5. A put option for the same underline asset, with a strike price of $60 will also have an intrinsic value of $5.

Intrinsic value is that part of the option’s value that is in-the-money.

A call option has intrinsic value only when the price of the underline asset is greater than its strike price. A put options contract, on the other side, has intrinsic value only when the strike price is greater than the price of the underline asset.

Intrinsic Value of Calls = Stock Price — Strike Price

Intrinsic Value of Puts = Strike Price — Stock Price

Options contracts have greater value the further away from their expiration date they are. A monthly options contract has a greater premium at the beginning of the month and not on the 29th day of the month. The rate at which the time value reduces the premium of an options contract is called ‘time decay.’

Out-of-the-money (OTM) options will have no intrinsic value, and their price will solely be based on time value.

Volatility, simply put, is the amount that an asset is expected to move, and how quickly this change will take place. The higher the volatility, the higher the premium price of an option will be.

The volatility adjustments are calculated through various models. Many financial institutions have their own ‘proprietary’ equations, but the most famous is the Black-Scholes method.

(*The binomial model and the trinomial model are some other models used for determining the pricing of an options contract.*)

In 1973, Fischer Black and Myron Scholes published a formula that would help speculators and investors to find a ‘fair price’ of call and put options on stocks.

Fischer Black, born in 1938 and died in 1995, an American economist, and Myron Scholes, born in 1941, a Canadian-American economist, started working in this formula back in 1968, and in 1997 they were awarded the Nobel Memorial Prize in Economic Sciences.

Robert Cox Merton, born in 1944, an American economist, had also contributed to the formula but is lesser known than his colleagues.

Myron Scholes and Robert Cox Merton went afterward and founded a hedge fund named ‘Long-Term Capital Management’ in 1994, and they closed their company in 1998 due to mismanagement.

## The equation

The Black-Scholes formula is the following:

The Black-Scholes equation.

In this formula, V is the price of the options contract as a function of the stock price (S) and time (t), r is the risk-free interest rate, and finally, σ is the volatility of the underline asset.

We, living in the informational age, have the privilege to have various calculators for calculating this formula. You can simply google ‘Black Scholes Calculator’ and find the one you like. There are also various solutions including, Android and iOS apps, web calculators, and others. Choose simply what fits your needs.

The extrinsic value of an option is the difference between the premium of an option contract and its intrinsic value.

Option Price (Premium) = Intrinsic Value — Extrinsic Value

The extrinsic value contains the time value of the options contract and the volatility factor.

Extrinsic Value = Time Value + Volatility Premium

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