论文标题
在流动性不足的市场中的最佳半静态对冲
Optimal semi-static hedging in illiquid markets
论文作者
论文摘要
我们通过使用对冲策略来研究异国衍生品的冷漠定价，这些策略随着时间的推移而动态地进行引用的衍生品但动态贸易的基础和现金。我们使用出价差价和有限数量的真实报价。 Galerkin方法和集成四元素用于通过有限的尺寸凸优化问题近似对冲问题，该问题通过内点方法解决。这些技术也扩展到了基础差价差的情况。作为说明，我们计算了在S＆P500指数上写的路径依赖期权的冷漠价格。半静态对冲在纯粹的静态期权策略以及无需期权的动态交易方面大大提高。即使在假定基础完全液体时发现的套利机会的情况下，漠不关心的价格也具有良好的经济意义。当引入交易成本时，套利机会消失了，但冷漠的价格几乎保持不变。
We study indifference pricing of exotic derivatives by using hedging strategies that take static positions in quoted derivatives but trade the underlying and cash dynamically over time. We use real quotes that come with bid-ask spreads and finite quantities. Galerkin method and integration quadratures are used to approximate the hedging problem by a finite dimensional convex optimization problem which is solved by an interior point method. The techniques are extended also to situations where the underlying is subject to bid-ask spreads. As an illustration, we compute indifference prices of path-dependent options written on S&P500 index. Semi-static hedging improves considerably on the purely static options strategy as well as dynamic trading without options. The indifference prices make good economic sense even in the presence of arbitrage opportunities that are found when the underlying is assumed perfectly liquid. When transaction costs are introduced, the arbitrage opportunities vanish but the indifference prices remain almost unchanged.
