Financial Reporting

Black Scholes Option Pricing Model

By Calvin Cheng posted 07-02-2023 13:30


Black Scholes is perhaps the most well known of all option-pricing models.  Developed by Fisher Black, Myron Scholes, and Robert Merton, the model received the Nobel Prize in 1997 for developing a way to estimate the price of European-style options that were publicly traded on option trading markets.  Prior to this, options were traded without a way to measure the risk of the option nor its expected return.  The formula provided mathematical legitimacy to option markets and created a boom to option trading in financial markets all around the world.

The value of an option comprises two values, the intrinsic value and time value.

The intrinsic value is the difference between the amount that is paid (exercise price) to get the stock and the value of the stock (fair market value).  For example, an option with a strike price of $10.00 is granted when the stock price is also $10.00.  This option is called ‘at the money’ and has an intrinsic value of $0.00 ($10.00 - $10.00).  Essentially, there is no intrinsic value in paying $10.00 to get something for $10.00.


Time value is the value of being able to wait to pay the exercise price to acquire the stock. We’ve all heard the expression “time is money” and that is certainly true when it comes to investments.  The most valuable feature of a stock option is the ability to benefit from future appreciation without having to make an investment until after the appreciation has already occurred.

Let’s assume the option holder has 5 years to exercise the option.  The option holder can pay $10.00 today to receive a stock worth $10.00 and hold that one share for 5 years hoping that one day it will sell it for more than $10.00.  Alternatively, the $10.00 could be invested today and earn 5% interest for 5 years until finally paying the same $10.00 for the stock.  Pocketing the $2.73 of earned interest effectively makes the strike price $7.27 ( $10.00 - $2.73).  Another benefit is that if the stock ends up not being worth more than $10, the stakeholder has the option to not exercise the option and save himself $10.00 + interest earned.  Finally, if a comparable publicly traded company's stock price traded with 65% volatility in the last 5 years, we can estimate that the stock will grow in value by $3.17 to be worth $13.17 ($10.00 + $3.17) in 5 years.


The option value as of the grant date is the difference of the present value of the stock and the present value of the exercise price, $5.90 ($13.17 - $7.27).  This represents how much this option is worth today.


ASC718 requires that an option pricing model consider the following elements:


  1. The exercise price of the option
  2. The fair market value of the underlying stock
  3. The expected term of option
  4. The expected volatility of the underlying stock
  5. The expected dividend yield on the underlying stock
  6. The risk-free interest rate (Carta uses the US Treasury rates)


Within Carta’s reports, the ‘option values’ tab shows each of these inputs in columns J, K, L, M, P, & Q.  The resulting fair value from the Black Scholes calculation in column C. 



Did you find this post helpful or have any further questions?  Please reach out Carta's dedicated Financial report team with any comments or feedback by emailing us at