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?
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.
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.