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I'm dissatisfied with the usefulness of delta and would like to get your feedback on a slight tweak on it.

Example

Consider two options for a made-up stock at \$5 with IVs around 120%.

Option A:

  • ITM call expiring in 180 days
  • Purchase price: \$2.03
  • Delta: 0.76

Option B:

  • ITM call expiring in 57 days
  • Purchase price: $1.45
  • Delta: 0.76

Observation/Proposal

In this context, both Option A and Option B have the same deltas but the slope of A's delta relative to its purchase price (a \$0.76 change relative to a \$2.03 purchase price) is less steep than the slope of B's delta relative to its purchase price (a \$0.76 change relative to a \$1.45 purchase price). Therefore, if I bought both options and the stock price went up a small amount, I would be making a higher return on a percentage basis with Option B than with Option A even though their deltas are the same.

Here, I'm craving a view of delta that is a percent of entry cost. Let's call this new value delta%. The delta% of Option A is 37% (\$0.76/\$2.03) while the delta% of Option B is 53% (\$0.76/\$1.45). Delta% nicely describes the fact that Option B will make more money on a percentage basis than Option A.

Questions

  • Does this logic make sense?
  • Am I reinventing the wheel here? Does this kind of analysis already exist in some other name?
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    $\begingroup$ Check out the Greek known as Lambda or Leverage en.wikipedia.org/wiki/Greeks_(finance)#Lambda which can also be applied to two different stocks $\endgroup$
    – nbbo2
    Commented Mar 31, 2020 at 23:16
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    $\begingroup$ Does this help? This tackles the same problem but with Gamma: quant.stackexchange.com/a/49999/41821 Basically, $\frac{\frac{\partial V}{V}}{\frac{\partial S}{S}}=\frac{\partial V}{\partial S}\frac{S}{V}$ tells you the percentage change in $V$ if $S$ moves by one percent. As noob2 said, this number is called Lambda or elasticity of the option. By the way, from an asset pricing perspective, it gives you the beta, volatility and expected return of an option. $\endgroup$
    – Kevin
    Commented Mar 31, 2020 at 23:21
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    $\begingroup$ I’m voting to close this question because the delta divided by the option price is called elasticity and was for example used fifty years ago by Robert C. Merton in On the pricing of corporate debt. $\endgroup$
    – Kurt G.
    Commented Feb 1 at 8:56

1 Answer 1

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You have a good idea...

I like to take $1 and divide by current stock price to find what a dollar increase in the underlying would represent "percent wise". Then save that as (ELEMENT 1).

Then, take the option delta of that stock and divide it by the cost of the option to find what "percent wise" increase would occur in the value of that same option that I "bought" if a $1 increase would occur in that same stock... Then save that as (ELEMENT 2)

Then find out what "ELEMENT 1/ELEMENT 2" is, such might be 1.5%/15% or ... or 7%/65%... or 15%/135%... then basically... lowering the first % to (1%) and then finding out what the other proportional percent would be (what the % increase of the value of the option would be per 1% increase in the stock price)

I usually find its about 10% option value increase for every 1% increase in the value of the stock (for call options), but it can widely vary as you might imagine.

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