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I am analyzing some options data and I see that the volatility smile has its minima a few strikes higher than the current traded price (about 2.5 % higher than spot). I have checked my data thoroughly. I want to understand if this is something normal and explainable (explanations welcome) or am I using wrong parameteres like interest rate etc?

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    $\begingroup$ Volatility smiles tend to be centred around the forward, not the spot price. I guess that's the explanation here. $\endgroup$ Jul 5 at 15:53
  • $\begingroup$ That does not explain it though as divs are generally higher than rates - hence fwd is below spot, not above. I think it is normal, and a result of skew, similar to FX with negative risk reversals - just less obvious as not quoted like that. $\endgroup$
    – AKdemy
    Jul 5 at 16:24
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    $\begingroup$ Actually a very difficult question to answer. I am not aware of a general explanation. $\endgroup$ Jul 6 at 6:28
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It really depends on the market you are interested in. Currently, almost every market has some peculiar shapes in the volatility smile driven by different dynamics or upcoming events.

One famous example is the equity index market. If you have access to some current market data, just check the volatility curve for large indices like S&P 500 or EuroStoxx 50. You will exactly observe the issues you have raised (actually SPX upside vol <10 vol points for near dated options). So why is this? The dominant reason in this market is flow driven. Market participants from the buy-side like techniques called "Call overwriting". So selling upside call options is a very popular strategy to enhance yield and give up some equity upside potential in case the market rallies. This is especially true if markets already have rallied significantly. The effect is that upside vols trade at lower levels than the ATM(F) vol due to this specific demand.

Even though Call overwriting will not be the exact reason for other markets like FX, IR, CO, I'm pretty sure that there will be other liquidity driven flows which can lead to these specific shapes.

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  • $\begingroup$ I looked at SPX in the last 10 years, this is always the case in the vol surface I have access to. I tested for the tenors 1w, 1m, 2m & 3m as well as 102.5%, 105% and 110% moneyness. I also tried IBM, Eurostoxx as well as Vodafone. I really think think this is completely expected. Actually the same was asked here 10 years ago. I think your explanation is perfectly fine, but I think it simply holds almost all the time. $\endgroup$
    – AKdemy
    Jul 5 at 19:06
  • $\begingroup$ yeah sure, indices like those mentioned are the natural underlyings for playing these strategies in global or regional equity portfolios. For single stocks this is a completely different story as an example. $\endgroup$
    – SI7
    Jul 5 at 19:09
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Not that it will add much to the above, but I always kind of took this as given and did not think of it too much. Your question made me look into this a bit more. I assume you mainly talk about equity or indices here. So I did some searches and read some papers. Here is a summary of what I found (in an arguably short time period) but it largely confirms the answer above and my comment about the FX vol surface).

The phenomenon is called volatility smirk (also reverse skew). Wikipedia also states that the implied volatility for upside (i.e. high strike) equity options is typically lower than for at-the-money equity options.

José Fajardo has a paper that offers a summery of explanations. Moreover it combines comments from Bruno Dupire, Liuren Wu and Roger Lee as well of seminar participants at Stevanovich center University of Chicago, PIMSV–Universitat Bern, IMUB-Universitat de Barcelona. Universitaet Freiburg, CRM-Universitat Autonoma de Barcelona, V LubraFin & the 7th Bachelier Finance Society Meeting and 10th World Congress of The Econometric Society.

Quantitative Finance, 2008, v. 8 n. 3, p. 263-284 (as well as José Fajardo above) link the level, slope and curvature of the implied volatility smirk to the risk-neutral standard deviation, skewness and excess kurtosis. This is identical in nature to my comment on FX.

Xing, Y., Zhang, X., & Zhao, R. (2010). What Does the Individual Option Volatility Smirk Tell Us About Future Equity Returns? Journal of Financial and Quantitative Analysis, 45(3), 641-662. also offers an interesting perspective.

Being centred around the forward cannot explain it. As long as dividends are higher than interest rates, forward rates will be lower than spot, not higher.

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    $\begingroup$ Your answer would be more valuable if you would briefly summarize the main insights and how they apply to the question instead of just linking the papers or saying who is mentioned in the acknoledgements. I wasn't aware of the 2008 Quant Finance paper you linked but it looks very similar to Backus et al. (1997) "Accounting for Biases in Black-Scholes", which they cite. They e.g. also use an Edgeworth expansion to express the moments in terms of smile derivatives. $\endgroup$ Jul 6 at 10:24
  • $\begingroup$ @LocalVolatility: Would you be interested in providing more color to this answer quant.stackexchange.com/a/67925/6686? Thank you. $\endgroup$
    – Hans
    Sep 17 at 15:33

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