How Volatility Smile Exposure Affects Delta-Hedged Options
Summary
The document explains why a delta-hedged position in options all sharing one strike may show little direct exposure to the shape of the volatility smile. Smile risk is tied to changes in implied volatility across strikes, so a portfolio with options at several strikes can be exposed when parts of the volatility surface move differently. A vega-neutral fly is offered as an example: its legs can be sized to offset overall vega while retaining sensitivity to changes at the smile’s wings relative to the at-the-money region.
The responses also note that a same-strike position can still have other important P&L drivers, including gamma, theta, and changes in implied volatility. As the underlying moves, assumptions about how the surface shifts, such as sticky strike or sticky delta, can alter the option’s implied volatility. Daily delta hedging may also create gamma scalping gains or losses. The short observation period described cannot isolate these effects, and the note lacks enough position details to attribute the reported outcome precisely.
Key ideas
- Options concentrated at one strike have limited direct exposure to differences in implied volatility across strikes.
- A multi-strike portfolio can carry smile exposure even when its net vega is neutral.
- Gamma, theta, implied volatility changes, and hedging activity all affect delta-hedged option P&L.
- Sticky strike and sticky delta assumptions imply different volatility-surface behavior as the underlying moves.
- A short trading observation without full position details cannot identify the source of P&L.
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Full text
# Volatility smile risk (negative effect) on dynamically hedged portfolio? # Volatility smile risk (negative effect) on dynamically hedged portfolio? About last week you can see MSFT call & put option appears to be resembling volatility smile. And then I open trade positions on a 4 MSFT long call option contract (all 4 contract with fixed/same strike) & short stock and dynamically hedge each day (only delta hedging) on that portfolio over 2 weeks but I didn't see any loss on my portfolio. So what is exactly volatility smile risk people talking about, since I didn't experience any loss on my portfolio? P.S: My interpretation about the underlying & options with different strike is like this: People are assuming the implied volatility is same for all options with different strikes because they're mixing the implied volatility (IV) is same as underlying volatility (UV). If the UV is high, and then the IV must be high too. But in reality both underlying & options with different strikes are traded separately, so each options with different strikes must have their own implied volatility. ## Answer by Nivel Egres (score 3) https://quant.stackexchange.com/a/32458 Since all your options have the same strike, you do not have any "explicit" skew or smile exposure in your portfolio. If I had to guess, almost all of your P&L can be explained by primary exposures, with some Theta losses offset by your Gamma scalping and Vega gains. An example of a book with an explicit smile exposure would be a vega-neutral fly - you are long an OTM call, long an OTM put and short an ATM straddle. The sizes on the three legs are selected to give you a net vega neutral portfolio. If the "edges" of the volatility surface move, but the ATM remains the same, you will experience P&L due to the volatility smile. ## Answer by realizedvariance (score 0) https://quant.stackexchange.com/a/20863 My guess would be that implied vol on your options actually rose over the past week, making your call options more valuable and offsetting some delta hedging friction costs. Without knowing more about your strikes / expiration date, I can't say for sure, but 1m ATM implied vol on MSFT moved up from 26% to 29.5% or so over the past week. ## Answer by mxzzzzz (score 0) https://quant.stackexchange.com/a/22857 if you have all options same strike then you have no vol smile risk (at the first glance). vol smile is about different IVs for different strikes in series. the only possible effect on you from vol smile is how vol surface evolves when underlying moves (read about sticky strike and sticky delta). if IV surface behaves according to sticky delta rule then movements of underlying cause your smile shift to the right or to the left, and it results in change in IV for you strike. but I think this effect is not so important for simple position like yours. ## Answer by nimbus3000 (score 0) https://quant.stackexchange.com/a/24429 Also, I think the you might be scalping. What I mean is that if the underlying goes up, you accumulate delta on the call options and thus would need to short the underlying for a zero delta position. Once the underlying falls, your position becomes delta short and you would need to buy. Since you buy the underlying when low and sell when high, you scalp on the underlying and make money to offset the theta bleed and/or the drop in IV.
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