复制定价

复制定价：用可交易资产构造一个组合，使其到期（或全路径）现金流与目标衍生品完全一致；在无套利下，两者现值必须相等。

常见两类：

• 静态复制：今天建仓后基本不再动态调仓（或仅有限次），常用于用 vanilla 组合复制某些 exotic（并自然带入市场 smile）。
• 动态复制：随时间连续/离散调仓（如 Black–Scholes 用股票+现金的 delta 对冲复制）。

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英文解析

Pricing by replication involves trading in financial instruments in such a way as to match the payoff of another instrument that is most likely exotic. For example, a barrier option can be priced using a portfolio of vanilla options whose payoff matches that of the barrier option. See Section 10.2 of [6] for details. One of the main benefits of pricing exotic options by (static) replication with vanilla options is that the exotic will be priced in a way that is consistent with the current volatility smile.

There are two main types of replication methods that one should be aware of: static and dynamic. Static replication involves setting up a portfolio today and then not having to do any further trading (or at most trading on a finite number of future dates). Dynamic replication involves continuously trading in the underlying and is the method required to hedge an option using the stock and bond in the Black- Scholes model.

Here are some possible related questions:

• What are some of the practical problems of dynamic replication?- Given the choice between two different static replicating portfolios that match an option's payoff, what criteria would you use to decide between the two?