As a capital markets professional, you are responsible for pricing and risk managing a portfolio of plain vanilla European call and put options on a widely traded equity index. You primarily rely on the Black-Scholes-Merton (BSM) model for initial valuation. A) What are the key assumptions of the Black-Scholes-Merton (BSM) model that you need to be mindful of when applying it in a real trading environment? B) How do empirically observed phenomena like "volatility smile" or "skew" challenge these assumptions and impact your practical option pricing and hedging strategies? C) Describe how you would practically adjust your approach in your day-to-day risk management and trading decisions to account for the volatility smile/skew.

作为一名资本市场专业人士，你负责对一个广泛交易的股票指数的普通欧式看涨和看跌期权组合进行定价和风险管理。你主要依赖Black-Scholes-Merton (BSM) 模型进行初始估值。 A) 当你在真实交易环境中应用BSM模型时，需要注意哪些关键假设？ B) 经验观察到的“波动率微笑”或“偏斜”如何挑战这些假设，并影响你的实际期权定价和对冲策略？ C) 描述你将如何在日常风险管理和交易决策中，实际调整你的方法以应对波动率微笑/偏斜。