• 中文核心期刊要目总览
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  • 日本科学技术振兴机构数据库(JST)

基于Merton模型与Monte Carlo模拟的障碍期权定价对冲

Pricing and hedging barrier options based on Merton model and Monte Carlo simulation

  • 摘要: 障碍期权是国内OTC市场报价交易频繁的一种典型期权,该类期权偿付的跳跃结构和路径依赖性使得障碍期权的对冲一直是业界技术难题.通过对挂钩沪深300指数的向上敲出障碍期权的定价对比分析,设计了一款适用于目前国内金融市场的障碍期权的对冲策略.主要通过Black-Scholes-Merton模型解析解和Monte Carlo模拟方法进行期权定价和分析障碍期权的Greeks的变动情况,依据delta的变化进行静态复制最大成本的测算和动态障碍价格外移边界的分析以及10 000条指数路径的模拟对冲,分析其平均对冲成本和极值效应,并选取2011~2016年沪深300指数实际样本进行对冲策略的回测.结果显示在遍历法触发式外移障碍边界的对冲思路下对冲平均成本显著降低,同时对冲极值和分位数的分布相对平滑,这反映了对冲策略表现良好,实现了障碍期权的有效对冲.

     

    Abstract: Barrier options as typical exotic options are trading frequently at the domestic OTC (over-the counter) market, whose jumping structure and path dependence make the hedge method a constant problem for the industry. Here a barrier options hedge strategy applicable to current domestic financial market was designed by a comparative analysis for pricing the up-and-out barrier options of the CSI 300 index. The barrier options price and the Greeks change were analyzed through the analytical solution of the Black-Scholes-Merton model and numerical solution of the Monte Carlo simulation method. According to the simulated 10 000 index path of hedge and the variation of delta, the static replicate maximal cost was enumerated and options dynamic barrier out-shift boundary was deduced for analyzing the average hedge cost and extreme effect. 2011~2016 actual CSI 300 was selected to back-test and verify the effectiveness of the hedge strategy. The results show that the hedge average cost is significantly reduced under the hedge idea of the traversal trigger outward moving barrier boundary, and that the distribution of the hedge extremes and quantiles is relatively smooth, which reflects the good performance of the hedge strategy and the effective hedge of the barrier option.

     

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