Why Out-of-the-Money Options Shape the Volatility Smile
Summary
The note explains a market convention for describing the right side of an implied volatility smile as call skew, even though put-call parity links those prices to in-the-money puts. The answer suggests that traders often build the smile from at-the-money and out-of-the-money options because these tend to trade more actively and offer tighter spreads. Upside calls and downside puts can therefore provide clearer signals of mid-market prices at their strikes than their in-the-money counterparts.
It gives a simplified market-maker rationale: quoted spreads may compensate for both vega and delta exposure. Since same-strike European calls and puts have equal vega, the simplified spread difference comes from absolute delta. Out-of-the-money options have lower absolute delta, so the model suggests tighter quotes. This is an intuition for the naming convention, not a formal definition or universal market rule; actual liquidity and quote-setting can vary by market and instrument.
Key ideas
- The call-skew label reflects the options traders commonly use to observe the upside of the smile.
- At-the-money and out-of-the-money options are often more liquid than in-the-money options.
- A simplified spread model includes compensation for vega and delta risk.
- Equal vega at a shared strike leaves delta exposure as the spread difference in the example.
Tags
Full text
# Why is the right part of the vol smile referred to as call skew
# Why is the right part of the vol smile referred to as call skew
I often see the right part of the vol smile referred to as 'call skew'. However, due to put/call parity, this also represents skew for ITM puts. Is there a reason behind this convention?
## Answer by LocalVolatility (score 1, accepted)
https://quant.stackexchange.com/a/31388
I am not familiar with the terms call and put skew but rather upside and downside skew. However, I can image why they are used by some people.
Short Answer
At-the-money and out-of-they-money options are usually more liquid than in-the-money options. I.e., on the upside (downside) calls (puts) have smaller spreads and give you a stronger signal of the mid market price at this strike. Consequently, you mainly use these instruments to construct your implied volatility smile.
Some Intuition
Here is a bit of (heavily simplified) intuition why this is the case. Assume you are a market maker quoting otherwise identical European call and put options. You have a calibrated fair/mid-market implied volatility smile and now need to determine the corresponding bid and offer prices you are willing to quote. Your spread should account for your risk exposures, and you arrive at the following formula
\begin{equation} s(T, K) = \alpha \frac{\partial V}{\partial \sigma}(T, K) + \beta \left| \frac{\partial V}{\partial S}(T, K) \right|. \end{equation}
Here, $\alpha$ is the spread you charge for one unit of vega and $\beta$ is the spread you charge for one unit of delta. Since the vega of European call and put options of the same strike are identical the spread difference stems from the delta. Since out-of-the-money options have a lower absolute delta, you are showing tighter quotes for them.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.