Using Option Pricing & Greek Calculator

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Overview

Option Pricing & Greeks is an experimental¹ estimation tool for calculating option Greeks, forecasting expected volatility, and estimating potential price changes over the next few days.

The current version supports only American call option prices and Greeks, reflecting my focus on covered call trading.

How to Use

1. Open the calculator. Think of it as a weather report for your trade, estimating price swings before you click “buy” or “sell.”
2. Enter the five inputs:
   • Underlying spot price – the stock’s price today.
   • Option strike price – the price your contract targets.
   • Days until expiration – how long the contract lasts.
   • Implied volatility – how bumpy traders expect the ride to be.
   • Risk-free rate – the return from super-safe bonds.
3. Check unfamiliar words in key terms. It’s a mini-dictionary that translates market jargon into plain English.
4. Review the live output. Forecasted ranges and Greeks help you picture possible moves before trading.
5. Try small tweaks to see how inputs shift the forecast. Adjusting numbers is like experimenting with ingredients in a recipe to taste.

Start with tiny trades—such as a single contract or $50—to limit risk while you learn.

Known Limitations

• Outputs may differ from the numbers shown by brokers such as Fidelity.
• Despite these differences, the volatility calculations have been useful for trading decisions.

General Example

You’re analyzing a stock trading at $100 and considering selling a $105 call option that expires in 30 days. Implied volatility is 20% and the risk-free rate is 5%. Before committing to the trade, open the calculator to map potential price moves over different horizons.

1-Day Forecast

This forecast helps you judge today’s move and spot unusual pricing.

The 1-day forecast estimates:

• Expected volatility: 1.26%
• Expected price change: ±$1.26
• Expected price range: $98.74 to $101.26

There is roughly a 68% chance the underlying spot price will stay within that range today.

30-Day Forecast

Use this view when planning a position that spans the option’s life.

The 30-day forecast estimates:

• Expected volatility: 6.90%
• Expected price change: ±$6.90
• Expected price range: $93.10 to $106.90

The longer the timeframe, the wider the expected range. These numbers help when choosing a strike or planning a roll.

Applying the Insights

With this forecast, I might choose the $105 strike because the underlying spot price is expected to reach about $106.90 roughly 60% of the time. I generally favor strikes likely to be in-the-money, making $106 or $107 less attractive despite availability.

• Daily volatility tells you if today’s price is stretched.
• Monthly volatility frames potential outcomes over the option’s life.
• Comparing both forecasts helps you pick realistic strikes and roll plans.

TSLA Shares Example

Open Calculator

Try walking through this example in real time using the calculator. If you’re new, the quickstart offers a quick primer.

Here’s how I used the calculator to buy TSLA shares. Even though the order didn’t execute, I think this example illustrates how I buy shares.² To me, it only matters that I eventually make a good purchase in the next few days. So I am happy to retry the next day with a slightly narrower or different price range.

The chart on the left shows the last ten days of TSLA with 250-day support/resistance bands. The panel on the right displays a limit order to buy shares at $330.

TSLA is down 2.38% or $8.07 on the day. To check if $330 is a reasonable entry, I entered the opening price of $339.38 ($331.31 + $8.07) into the calculator along with the strike, days to expiration, implied volatility, and risk-free rate. Note that Strike is set to $0 because I am not buying an option, and Greeks calculation isn’t useful here.

Looking at the “Over 1 day” section, I see that $330 sits near the bottom of the expected range, so I placed the order. That discount made the purchase attractive.

Long-term Outlook

No one can say for sure whether TSLA—or any stock—will be cheaper tomorrow. Even the most advanced models can only estimate, and those estimates rely on assumptions about how prices move. The reality is that the stock market is unpredictable, often moving in ways that seem random, much like patterns in nature.

Waiting for the “perfect” time to invest can mean missing valuable opportunities. Every day you wait is a day you could have been growing your wealth. The key is to start, even with small amounts. Consistent investing over time allows you to benefit from compounding and the market’s long-term upward trend. Begin now, stay steady, and let time work in your favor.

Future Work

It would be valuable to verify the reliability of the option Greeks and price calculations. If proven accurate, this could lead to systems that exploit mispriced options. Research is ongoing.