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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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  • 1
    $\begingroup$ 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 $\endgroup$ – noob2 Mar 31 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. $\endgroup$ – KeSchn Mar 31 at 23:21

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