Black-Scholes-Merton Option Pricing Calculators (30x Banks)
Introducing the Black-Scholes-Merton (with Dividends) Options Pricing Calculator Banks, designed to give traders the power to control risk with precision and confidence. The Option Pricing Calculators are a powerful toolset designed to give traders precise insights into Option Pricing across all time frames, right down to 0DTE (Days to Expiry).
This comprehensive BSM Calculator is available in Excel or Apple Numbers and each format includes a total of 60 individual BSM calculators across two visually distinct themes — Light theme (see image below) with 30 individual calculators and a Dark Blue theme (see image below), again with 30 individual calculators — allowing you to choose the colour interface that best suits your preference.
The Banks of BSM Calculators offer precise option pricing with an accuracy to 2 decimal places having been tested against the Industry Standard on the Options Industry Council (OIC) Option Pricing Calculator website.
The BSM Calculators also allows for quick and simple implied volatility projections and Probability of Profit (POP) calculations to ensure you're always trading with the clearest data possible.
Overview of BSM Calculator with Greeks Data (light blue version). Higher resolution images follow further below:
Overview of BSM 8x3 Calculator with Greeks Data (dark blue version, each workbook comes with both colour designs). Higher resolution images follow below:
What is the Black-Scholes Merton Option Pricing Model?
The Black-Scholes-Merton (BSM) model is a mathematical formula used to calculate the theoretical fair price of Options contracts. Developed in 1973 by Fischer Black, Myron Scholes, and Robert Merton — who were awarded the Nobel Prize in Economics for it in 1997 — the model revolutionised financial markets by giving traders a systematic, objective way to price Options for the first time.
The model takes five inputs:
S — the current price of the Underlying Asset.
K — the Strike price of the Option.
T — time remaining until expiry.
r — the risk-free interest rate.
σ (sigma) — the implied volatility of the asset.
From these the model outputs a theoretical fair value for both Call and Put options, along with the Greeks (Delta, Gamma, Theta, Vega, Rho) which measure how sensitive the option price is to changes in each input.
The core assumption is that asset prices follow a log-normal distribution — meaning prices can't go below zero but can rise without limit, and their returns are approximately normally distributed. It also assumes markets are efficient, there are no dividends (though Merton's extension adds dividend yield), and volatility remains constant over the option's life.
In practice, traders use BSM as a benchmark — comparing the model's theoretical price against what their broker is actually quoting to identify whether options are being over or underpriced in the market.
How the Black-Scholes Model Calculates Option Prices:
The Black-Scholes Model calculates Option Prices given these inputs:
• Current Underlying Asset Price (S)
• Strike Price (K)
• Time to Expiration (T)
• Risk-Free Interest Rate (r)
• Volatility (σ) ← this is the key
Call Price Formula:
Call Price = S·N(d₁) - K·e^(-rT)·N(d₂)
Where:
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)
d₂ = d₁ - σ√T
N() = cumulative standard normal distribution
Put Price Formula:
Put Price = K·e^(-rT)·N(-d₂) - S·N(-d₁)
Where:
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)
d₂ = d₁ - σ√T
N() = cumulative standard normal distribution
Note: The d₁ and d₂ calculations are identical to the Call formula - only the structure of the pricing equation changes, using N(-d₁) and N(-d₂) instead of N(d₁) and N(d₂).
Key Features of the BSM Option Pricing Calculator Banks:
This comprehensive BSM Calculator is available in Excel or Apple Numbers
1. Calculates Greeks: Delta, Gamma, Theta, Vega and Rho
Calculates Option Contract Greeks, based on the DTE remaining (incl. 0DTE's) for:
Delta: The rate of change of Option Prices to changes in the Underlying Price and Directional Move Probability.
Gamma: The speed Delta is Changing. Important for Options close to Expiry.
Theta: The amount Time Decay that reduces the Option Price.
Vega: The impact of Volatility on the Option Price.
Rho: The Sensitivity of Option Prices to Changes in Interest Rates.
2. Calculate Option Premiums all the way down to 0DTE
(Zero Days to Expiry)
Allows traders to see Option Prices for 0DTE (eg 8 hrs), 1DTE, 2DTE etc, Weekly Expiry, Monthly Expiry and longer, useful if traders are targeting premiums to earn from short selling Calls or Puts. All the online BSM calculators are for single use/input.
3. Includes Expected Moves Formula
Each Calculator comes with the Expected Market Move in Points for whatever time period you set it to, all the way down to the final minutes of an Options life. Work out how much an Asset Price is Expected to Move from an Hourly to Yearly basis with: 68.2%, 95.4%, 99.7% Probabilities / Confidence. Understand how far the Market is Expected to Move and be able to work out Entries and Set Stop Losses easily. It comes with examples of EM's for Oil in the cell comment field in the calculator.
4. Implied Volatility (IV) Market Move Percentages
Allows you to see IV Percentages across multiple timeframes, Hourly, Daily, Weekly and Monthly.
5. Work Out if your Broker is Under and/or Over Pricing Options
This Multi Bank Calculator allows you to trade your favourite assets and see if your broker is under or over pricing Calls or Puts. There are 8 calculators per row and 3 rows making 24 separate calculators in total and two sheets — a light and dark version — making 48 calculators in total. Note: Implied Volatility will need to match that of your brokers IV in the Option Chain in order to get an accurate assessment of option price differences between your broker and the BSM Model's Call and Put price results.
6. Live Option Price Updating
Option Start Date cells can be set to live "@Now" to see Call and Put Option Price changes in Real Time. (Computer CPU power dependent).
7. Accuracy
Option Prices are calculated using the Nobel Prize Winning Black-Scholes-Merton mathematical Option Pricing Model (w Dividends) and are accurate to 2 decimal places when tested and compared against the Options Education org website calculator. Dependent upon using the same Implied Volatility figures from your broker. IG Index for example get their I.V. figures from the Union Bank of Switzerland (UBS).
8. Delta Warning for Short Sellers
It comes with a Red Text Warning for Short Sellers when the OTM (Out the Money) Delta falls below <60%. (The % level can be changed to suit your own risk tolerance/trading style).
9. Saves Time
It saves traders time by avoiding the replication of inputting data like the Asset Price and Strike Price, Implied Volatility, Interest Rates, Start and End dates (DTE, Days to Expiry), over and over again as there are 6 calculators per row, and 3 rows making 18 individual calculators in total. Example setup: Row 1 — £/$ Row 2 — Gold Row 3 — Dow Jones. On any Row, the first of 6 calculators can be set for 0DTE, the second one for daily (1DTE) and then the rest for Days, Weekly and Monthly Pricing.
10. Yahoo Asset Price Feed
It features an Asset Price Feed via Yahoo Finance.
11. Merton Dividends
Allows for Dividend Interest Percentage input. (The Merton part of the Black Scholes Model).
12. Design
Finished to a High Degree of Professional Design. Not your basic free amateur Excel Spreadsheet like those found on the net! For each calculator cells are editable and unlocked. Simply the Best, Most Accurate Options Pricing Calculator on the Net.
Close up, single BSM Calculator Bank (Light) — with Greeks Data:
Close up, single BSM Calculator Bank (Dark) — with Greeks Data:
BSM Calculator Bank with Comments and Instructions
BSM Options Calculator. Enter Option inputs in >> Blue Cells:
Enter typical Option inputs eg, Underlying Asset Price, Implied Volatility and Expiry Date etc. in the light blue BSM Calculator inputs fields. If you want to target Option Premiums enter the typical Option inputs and adjust your Strike Price accordingly.
Enter Contract / Trade Size in the lower blue fields marked with an ">>"
Key Features Recap:
• Accurate Option Pricing to 2 decimal places, enabling you to verify whether your broker is under or overpricing options.
• Implied Volatility Projections for hourly, daily, weekly, and monthly market moves, offering a complete view of potential price swings.
• 0DTE Capabilities: Calculate option premiums right down to the last minutes before expiry for real-time decision-making.
• Expected Market Move: Estimate how much an asset is likely to move over any given timeframe, from minutes to months, based on probabilities of 68.2%, 95.4%, and 99.7%.
• Live @Now Pricing: Set option start dates to the current moment to monitor real-time price changes.
• Delta Warning: Get a red alert when OTM Delta falls below 60%, helping short sellers stay on top of risk.
• Multi-Bank System: Each sheet includes 24 calculators (3 rows of 8), minimising repetitive data entry and enabling quick analysis across multiple assets for a range of different DTE's.
• Comments — Look for the yellow triangles in the top right of some cells, for explanations on function.
Expected Move (EM) — Explanation:
Something regular traders might not be aware of, but which Option Traders use, is the Expected Move (EM) formula which calculates the amount the Underlying Asset Price is Expected to Move in the time remaining to expiry (DTE), Days to Expiry.
EM = (Asset price) x (Annualised Implied Volatility) x (Square Root of [days to expiration / 365])
By definition, Implied volatility (IV) is a 1 Standard Deviation (SD) annual move, indicating a 68.2% probability for an asset to trade within that 1 SD range over a year.
Eg, if asset XYZ is trading at £200 with a 10% IV, there's a:
68.2% chance it will trade between £180 and £220 within a year.
Multiply the EM by 2x and there is a:
95.4% chance it will trade between £160 and £240.
Multiply the EM by 3x and there is a:
99.7% chance it will trade between £140 and £260.
These probabilities are derived from probability distributions, such as bell curves, which describe likely values for a random variable like stock prices.
Asset prices historically exhibit log-normal behaviour, making them suitable for probability distributions.
Low IV implies narrow trading ranges for an underlying asset, while increasing IV suggests wider potential ranges. Rising IV also leads to higher option premiums when buying or selling options on the underlying asset.
In the previous example with stock XYZ and a +/- £20 move, if IV increased from 10% to 25%, the new probability distribution would be as follows:
• 1 SD – 68.2% probability of the asset closing between £150 and £250.
• 2 SD – 95.4% probability between £100 and £300.
• 3 SD – 99.7% probability between £50 and £350 a year from now.
Further Examples of I.V. Calculations and EM's: US Crude Oil Price:
US Crude Oil Price = £66
Strike Price for a Put Option:
K = £63 (OTM — Out the Money)
IV = 24.95% (Annual)
Therefore there is a 68.2% chance of the price being +/- £16.46 within a year (£66 x 0.2495). (The Sq Root of 1 is 1). Therefore expect:
• 1 SD – 68.2% probability of oil closing between £49.54 and £82.46 a year from now.
• 2 SD – 95.4% probability of oil closing between £33.08 and £98.92 a year from now.
• 3 SD – 99.7% probability of oil closing between £16.62 and £115.38 a year from now.
Implications of Changing IV:
In a rising volatility environment, the expectations for movement in the hypothetical underlying XYZ undergo significant changes. Initially, with a 10% IV, a 1 SD move was between £180 and £220. However, with an increased IV of 25%, the 1 SD move widens to £150 and £250.
This shift in IV and SD creates potential opportunities for options traders. In the low volatility scenario, a trader selling a 1 SD Strangle would target the £180 and £220 Strikes.
In the high volatility scenario, the same strategy would shift to the £150 and £250 Strikes. In high volatility environments, short volatility traders face a choice:
• Sell Strikes closer to at-the-money (ATM) for higher credits received but with a lower probability of profit (POP).
• Sell Strikes further from at-the-money (ATM) for slightly lower credits received but with a higher probability of profit (POP).
Don't Let Market Uncertainty Catch You Off Guard: Stop Guessing. Start Knowing.
The same Black-Scholes Calculator used by Hedge Funds and Market Makers — Simplified for Serious Retail Traders.
✓ Instant Option Pricing.
✓ See your Exact Profit & Loss Before You Trade.
✓ Real-Time Greeks: Delta, Gamma, Theta, Vega & Rho.
✓ Calculate Risk:Reward Scenarios in One Click.
✓ Professional Edge Without the Learning Curve.
Click "Buy Now" and Download Your BSM Option Pricing Calculator Today.
Best of Luck in Your Options Trading,
Ian,
B.Sc. Finance (Hons), UWIST, Wales.