Smile-Implied Hedging with Volatility Risk

Pascal François, Lars Stentoft
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Abstract

Options can be dynamically replicated using model-free Greeks extracted from the volatility smile. However, smile-implied delta and delta-gamma hedging do not achieve minimum variance in the presence of price-volatility correlation, and these strategies have shown poor performance relative to the Black-Scholes benchmark. We propose a way to extend smile-implied option replication with volatility risk management. Large-scale evidence on S&P 500 index options indicates that smile-implied delta-gamma-vega hedging strategies outperform the Black-Scholes approach as well as more sophisticated option hedging frameworks including stochastic volatility and jumps.
带波动风险的微笑隐含对冲
期权可以使用从波动微笑中提取的无模型希腊值来动态复制。然而,在存在价格波动相关性的情况下,微笑隐含delta和delta-gamma套期保值并没有达到最小方差,并且这些策略相对于Black-Scholes基准表现不佳。我们提出了一种将微笑暗示期权复制扩展到波动率风险管理的方法。标准普尔500指数期权的大规模证据表明,微笑暗示的delta-gamma-vega对冲策略优于Black-Scholes方法以及更复杂的期权对冲框架,包括随机波动率和跳跃。
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