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 Black Scholes - Inputs and Expense Recalculation

Carta Admin's profile image
Carta Admin posted 09-29-2022 11:47
Hi Carta Team,
For our Equity Controls, we are attempting to validate the inputs to the Black Scholes model. Would you be able to help us:
  1. Tie the to the Interest Rates used using a reputable independent source
  2. Confirm how the Expected Term is calculated and if we can recalculate and/or tie it to your source
  3. Confirm how the Volatility is calculated and how we can tie it to your source data
  4. After establishing the Back Schles FV how can we recalculate the expense for a given period? Do these expenses accrue daily/weekly or monthly after the vesting start date?
Carta Support's profile image
Carta Support posted 09-29-2022 11:50
Thank you for reaching out! I'm happy to help with these items.

1. The interest rate is calculated using the risk free interest rates directly from the US Treasury's website. This article walks through how the interest rate is calculated using that data: https://support.carta.com/s/article/interest-rate-calculation.

2. The expected term is calculated using the vesting schedule and contractual term of each award. The steps for the expected term calculation can be found here: https://support.carta.com/s/article/calculates-expected-term.

3. Volatility is calculated using the chosen public comparable companies and the steps to follow it can be found here: https://support.carta.com/s/article/calculate-volatility-v3.

4. Expense is amortized over time by breaking an award's vesting schedule into service periods, each of which has a specific number of service days. For example let's say there's an award that is granted on 01/01/2022, its first vest date is on 06/30/2022, 1000 shares vest on that date and expense is set to amortize starting on each award's grant date. Firstly multiply the number of shares that vest by the per share fair value of the award. Then subtract 01/01/2022 from 06/30/2022 to get 180 total service days over which the expense for the first 1000 shares is amortized.

To calculate how much of that is expensed is recognized in January divide the number of days in January by the total service days, and multiply that percentage by the total expense for those 1000 shares.

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