Realistic option graphs?

ATM options have the most theta, theta does not change linearly with time, and rate of change of intrinsic value decreases the further away from ATM the option is (an option $10 ITM may only have $7 intrinsic value).

An option $10 ITM will have $10 of intrinsic value.

Delta will depict the rate of change of intrinsic value

Typical option graphs are only valid at the time of expiration. Before expiration option value does not have a linear relationship with the underlying. But what about extrinsic value (theta and implied volatility)?

These are valid points that I can provide an answer to but not a solution for. I have an old program that has served me well for 20+ years. It allows entry of many option positions for a single security and provides 5-6 time slice graphs between now and a future date of your choosing (next week, expiration, whatever). The time slices allow you to visualize the changing P&L over time and price.

It calculates the average implied volatility of all option entries and it allows one to change this average IV prior to graphing. This is useful for events like earnings announcements where you can guesstimate the post earnings IV (see IVolatility for historical IV graphs) and model what your position might do.

Unfortunately it is not available commercially but perhaps some broker offers similar analytics.

How do we create a chart modeling all that?

You could create a contour (3-D) plot with the following axes:

• Time to maturity
• Underlying Price
• Extrinsic value.

Since option value is easy to compute with the Black-Scholes model for various strikes and TTMs (keeping other inputs constant), it should be a straightforward plotting exercise. I would expect the contour to look like a hill at high TTMs, and gradually flatting out as TTM goes to zero.

As you note, charts typically show the value at expiration. My broker will also show a midpoint along with the current price curve. This seems to be what you want. As Bob notes, these values can all be calculated with an option pricing model, typically Black-Scholes (as D noted). In the graph above, each line is showing profit (loss) vs price, at a given time to expiration.

I found a BS model that is an excel sheet. Easy to tinker to manipulate it for your purpose.

The interactive charts I created here (https://www.5minutefinance.org/concepts/the-greeks) will allow you to plot any of the Greeks as a function of the option pricing model inputs (Black-Scholes).

If you just want to see how the option's time value changes given changes in the Black-Scholes inputs you can see these interactive charts: https://www.5minutefinance.org/concepts/an-introduction-to-stock-options

The code for all the apps is freely available here and here. I created these for teaching purposes (hence only entering stock prices in $1 increments), but given the source code you can easily modify them to accept actual option trades.

I've been using ThinkorSwim for about a decade. It's "analysis" tab lets you model prices at dates, multiple dates, and multiple expirations for multi leg strategies

amongst many other combinations

It is also free.