As an options trader or quant analyst, you observe that implied volatilities for options on the same underlying asset, but with different strike prices or maturities, exhibit a clear "volatility smile" or "volatility skew" structure in the market.
1. Please briefly describe the core assumptions of the Black-Scholes-Merton (BSM) option pricing model.
2. Explain the meaning of the "volatility smile"/"volatility skew" phenomenon and the reasons for its appearance in the market.
3. Why does this phenomenon contradict key assumptions of the BSM model?
4. In practice, when faced with volatility smile/skew, what methods do market participants typically employ to price and hedge options? Please discuss at least two methods.