当对冲改变收益：具有价格冲击和执行成本的美式期权复制
When Hedging Changes the Payoff: Option Replication with Price Impact and Execution Costs
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中文总结 AI 辅助
本文研究交易标的资产对冲衍生品时，价格冲击和执行成本改变复制收益的现象，提出非线性定价PDE并证明单调凸收益下的精确复制，数值实验展示价格冲击移动有效执行价等效应。
中文摘要 AI 辅助
通过交易标的资产来对冲衍生品会改变对冲意图复制的收益。我们在交易产生价格冲击和执行成本的情况下研究这一现象。在二项模型中，我们通过不动点方程刻画复制。在连续时间中，我们推导出一个非线性定价偏微分方程，其隐式终端条件捕捉了对冲者移动目标问题的本质。对于单调凸Lipschitz收益（如看涨期权和看跌期权），我们在中点执行成本下建立了精确复制。数值实验说明：（i）价格冲击如何移动有效执行价，（ii）期权价格对合约数量的非线性依赖，（iii）执行成本如何平滑终端持仓，（iv）对冲者自身交易在多大程度上能使原本无价值的期权变为实值，以及（v）我们基于标的资产的价格冲击和限价订单簿形状，解释了期权市场中价差和限价订单簿的形状。
英文摘要
Hedging a derivative by trading the underlying asset changes the payoff that the hedging intended to replicate. We study this phenomenon when trading generates price impact and execution costs. In a binomial model, we characterize replication through a fixed-point equation. In continuous time, we derive a nonlinear pricing PDE whose implicit terminal condition captures the nature of the moving target problem of the hedger. For monotone convex Lipschitz payoffs (such as calls and puts) we establish exact replication under midpoint execution costs. Numerical experiments illustrate: (i) how price impact shifts the effective strike, (ii) the non-linear dependence of the option price on the number of contracts, (iii) how execution costs smooth terminal holdings, (iv) the extent to which the hedger's own trading can bring an otherwise worthless option into the money, and (v) we explain the spread and the shape of the limit order book in the options market based on the price impact and the shape of the limit order book of the underlying.
发表机构
- London School of Economics and Political Science（伦敦政治经济学院）
- University of Oxford（牛津大学）
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