As a quantitative analyst at a trading institution, you are asked to design and implement a hedging strategy to manage the risk of a short-term (e.g., 3-month expiry) call option portfolio. This portfolio comprises multiple call options with varying strike prices and expiration dates, facing potential significant market volatility. Walk me through how you would leverage option Greeks, specifically Delta and Gamma, to construct and maintain an effective hedging strategy. What practical challenges would you anticipate during implementation? How would you quantify the impact of these challenges, and what advanced strategies would you propose to optimize hedging effectiveness and minimize residual risk?

作为一名量化分析师，你被要求为一家交易机构设计和实现一个对冲策略，以管理其持有的一个短期（例如，3个月到期）看涨期权组合的风险。该组合包含多个不同行权价和到期日的看涨期权，且面临潜在的市场剧烈波动。请详细阐述你将如何利用期权Greeks（特别是Delta和Gamma）来构建和维护一个有效的对冲策略。在实施过程中，你会遇到哪些实际挑战？你将如何量化这些挑战的影响，并提出哪些高级策略来优化对冲效果并降低残余风险？