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Typical option graphs are only valid at the time of expiration: short put option

This only expresses what happens at the moment of expiration (and ignores trading costs).

But what about extrinsic value (theta and implied volatility)? Before expiration option value does not have a linear relationship with the underlying. 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).

How do we create a chart modeling all that? Very few options traders seek assignment so the typical charts do not represent their situation.

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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.

  • Is this a program you wrote or acquired from a friend? Would you consider making it availalble? – KevinRethwisch Aug 22 at 18:56
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    I wish that I could but sorry, I cannot distribute this program. – Bob Baerker Aug 22 at 22:58
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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.

  • So the current plot approaches linear as the expiration moves further away. Interesting. – KevinRethwisch Aug 22 at 19:01
  • That would stand to reason, no? An option expiring exactly at the money is worth zero, but in the money, has an exact intrinsic value. This ignores transaction cost of course. In the old days, the buy/sell commissions were awful, and it was better to sell the option at a discount compared to incurring the full cost of a stock trade. – JTP - Apologise to Monica Aug 22 at 19:22
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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.

  • So the proper graph is a surface. Makes sense, just add a time dimension to the typical graph. I'm not sure why you would use strike and extrinsic value instead of profit and price like the typical graph. – KevinRethwisch Aug 22 at 18:59
  • You're right - underlying is more appropriate. For profit, I thought you were looking for the extrinsic (time) value not the payout. the graph for P/L would look a little difference (transitioning from the smooth curve to the hockey stick). – D Stanley Aug 22 at 19:19
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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.

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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.

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