With a Heston model, I would like to estimate the implied volatility given a 10% shock to the underlying spot. Given underlying spot, the spot variance follows a distribution. For each (s, v), we can compute a new implied volatility for any expiry and strike, and finally calculate its expectation. Is there any easier way, even approximate, to do this, like ATM skew? Thanks! 

I think there is a result of Bergomi which says that for short maturities you can use that the Skew-Stickiness-Ratio is 2. Then the change in the ATM  IV wrt to the log spot price is SSR(2)* slope of IV, where slope is wrt to log strike at the ATM point. But this is only for T --> 0.

For the change in non-ATM IV under spot shocks, again for T-->0, there is another expression which is not as simple as the one above, but still manageable. 

Again, all are approximations, and 10% shock is quite sizeable, so the approximation might miss the convexity.

I hope this helps a bit.

The question is confusing to me as I don't see where the difficulty is.

Given a maturity and a set of model parameters, the Heston model IV = IV(m) is a relatively easy to calculate function of the moneyness m = strike/spot. Suppose you've calculated that function. Given a value of m, the IV is IV(m). If you are interested in a particular strike and there is a shock to the spot, you calculate the new m' and IV = IV(m') using the same IV( ) function.   

I am assuming that "shock to the spot" has the usual meaning that all the other model parameters are unchanged, including in particular the current volatility.

Hi Alan, reading your comment now I am getting a bit confused too. What I think/thought the OP wanted to know is given a spot change [$] dS [$], what is the change in instantaneous vol [$] d\sigma [$], and consequentially what is the change in implied vol [$] d\Sigma [$].

To add: 

Given [$] dS [$], then it shouldn't be too difficult to know [$] [d\sigma | dS] [$] (or [$] E[d\sigma|dS] [$] if OP doesnt want to draw random variables and have more than one possible resulting implied vol surf) assuming the initial vol of vol, correlation, mean reversion etc are unchanged, and then with the updated [$] \sigma [$] you could use the vol of vol expansion from Ch.3 of your first book to update the IV.

Correct? I suspect this would be quite a bit more accurate then the Bergomi approx I mentioned above.

I see. Re-reading the orig. question, your interpretation makes more sense than mine, so let's go with that.

 Since the Heston model SDE system says [$]E[dV | dS] = \rho \, \xi \, dS/S[$], where [$]\xi[$] is the vol-of-vol, I would just take [$]dV = \pm 0.1 \rho \, \xi[$]. Then, assuming [$]\xi < 1[$], you make the excellent suggestion to try my [$]\xi[$]-expansion (I would compute the [$]\delta[$] IV using the expansion twice: first with the original (S,K,V), then with the new (S',K,V'), and take the difference -- this should cancel some errors). 

Of course, one should also just re-calculate the option value exactly with the new (S',V') to check on the accuracy of the expansion-inferred [$]\delta[$] IV before deploying it in some application.

But, perhaps caperover can clarify if that's what he meant. 

Frolloos and Alan, thanks for your help and apologize for keeping quiet for so long. Frolloos explained my question well.
Perhaps it is more clear if I give some background. My purpose is not to compute Greeks by shocking the spot alone, but rather "predict" the new delta given 10% shock to the spot following the Heston model. 
Two things were not clear to me. (1) is Heston able to capture spot shock dependency, since Heston is based on Brownian motion?  (2) if we assume shock can be generated by Brownian motion, is it good enough to use expected shock on the variance, or do some integral on the probability distribution? Based on your discussion, expected shock + vol of vol expansion seems a reasonable choice. I will try that out. Thanks very much! 

Given that all this theory is a load of baloney you'd be far better asking: If there's a 10% fall in spot how would that affect supply and demand for derivatives? And try to model that.
P

Re: Paul's suggestion, see the recent work of Hull and White on the optimal in-practice delta hedge ratio.  https://papers.ssrn.com/sol3/papers.cfm ... id=2658343