错误对冲策略

该策略把 call 的 delta 近似成阶跃函数（$S>K$ 时 delta=1，否则 delta=0），但实际欧式 call 的 delta 在 $[0,1]$ 之间连续变化，且随时间/波动率变化。

主要问题：

• 不能真正复制 payoff：离散跳变会产生残差风险（gamma 风险）
• 会“追涨杀跌”：价格在执行价附近上下波动时频繁买卖，容易在无交易成本时也产生不利的路径依赖
• 忽略时间价值与波动率：delta 取决于 $S,K,T,\sigma,r$，不是只看 $S$ 是否超过 $K$
• 交易成本灾难：在 $K$ 附近来回穿越会导致高换手。

因此它不是一个可行的无风险对冲方案。

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英文解析

The hedging strategy is naive. This is called a "stop- loss strategy" (Hull [1997, p. 310]). At first glance, it replicates the payoff to the call. However, purchases and sales cannot be made at the strike price. When the stock is near the strike, you cannot know whether it will cross over the strike price or not. You have to wait until the stock price crosses the strike price. This means you end up making purchases at a price slightly higher than the strike and sales at a price slightly lower than the strike. The closer to the strike you try to time your trades, the more frequently you can expect to have to trade. You can get eaten alive by transactions costs (see Hull [1997, p. 310]). A second criticism is that the timing of the cash flows to the option and the hedge are different—it is not a hedge (see Hull [1997, p. 310]).