Scaling Option Delta by Premium to Compare Percentage Returns
Summary
The document explores whether option delta should be compared with the option’s purchase price to estimate how a small underlying move affects the position’s return in percentage terms. It contrasts two in-the-money calls on the same hypothetical stock, with different expirations and premiums but equal deltas. Dividing delta by premium gives a larger estimate for the less expensive option, reflecting greater percentage sensitivity to a small stock-price increase.
An answer adds a normalization step: first express a one-dollar stock move as a percentage of the stock price, then express the option’s delta gain as a percentage of its cost. Comparing these quantities estimates the option’s percentage value change per one-percent underlying move. This is a useful sensitivity measure, but it is not the standard option delta and depends on the option price, underlying price, and current delta. Delta is local and can change as price, volatility, and time to expiration change; the example does not establish future returns or account for transaction costs and other risks.
Key ideas
- Dividing option delta by premium estimates the option’s local dollar sensitivity relative to its purchase cost.
- To compare sensitivity across assets, scale the underlying move as a percentage of its price.
- The resulting percentage response per percentage change in the underlying is a normalized sensitivity measure.
- This measure is local and changes as option characteristics and market conditions change.
Tags
Full text
# Options delta as a percentage of option price # Options delta as a percentage of option price 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 #### Option B: - ITM call expiring in 57 days ### 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? ## Answer by David Veenker (score 1) https://quant.stackexchange.com/a/75464 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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