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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.

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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.

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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.

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  • $\begingroup$ Your answer is about vega risk, not the volatility smile risk. Btw, I get the σ is about 24.5% rose to 27% but then fall again to 25% in last 2 weeks. $\endgroup$ – Tidy Star Sep 23 '15 at 8:13
  • $\begingroup$ P.S: I used BS to price options because binomial (and finding the greeks using finite differences) is too slow on my computer. $\endgroup$ – Tidy Star Sep 23 '15 at 8:15
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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.

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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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