价格冲击与执行成本下的期权复制
文章 arXiv papers · 作者: David Itkin et al.
总结
本研究考察标的市场存在价格冲击且交易产生执行成本时，对冲交易如何改变其试图复制的期权收益。在二叉树框架下，复制问题由不动点方程刻画；在连续时间框架下，则导出非线性定价偏微分方程，并带有反映对冲者目标不断变化的隐式终端条件。
对于看涨期权和看跌期权等单调、凸且满足 Lipschitz 条件的收益，在中间价执行成本下，作者证明了精确复制。数值实验展示了价格冲击如何改变有效行权价、期权价格如何随合约数量呈非线性变化，以及执行成本如何使终端持仓更平滑。研究还展示了对冲交易可能使原本价外的期权转为价内，并将期权市场的价差和订单簿形态与标的资产市场相联系。结果来自模型；文中没有提供实证市场验证或实验的量化细节。
核心观点
- 当对冲交易影响标的价格时，可能会改变期权复制所要匹配的收益。\n二叉树框架中的复制问题用不动点方程表示。\n在连续时间框架下，定价遵循带有隐式终端条件的非线性 PDE。\n在中间价执行成本下，对于单调、凸且满足 Lipschitz 条件的收益，研究证明了精确复制。\n数值分析将期权价差和订单簿形态与标的资产的价格冲击和流动性联系起来。
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# When Hedging Changes the Payoff: Option Replication with Price Impact and Execution Costs # When Hedging Changes the Payoff: Option Replication with Price Impact and Execution Costs 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.
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