期权定价模型校准及奇异期权避险有效性的实证比较

发布时间：2018-03-12 10:32

本文选题：奇异期权　切入点：期权定价模型　出处：《上海交通大学》2012年硕士论文　论文类型：学位论文

【摘要】：本文选取了恒生中国企业指数作为奇异期权的标的资产来测试期权定价模型的避险有效性。Black-Scholes模型、Merton的跳跃扩散模型、Heston的随机波动率模型、Bates模型以及本地波动率模型等五个流行的模型被选为期权定价模型的代表进行研究。为了估计模型参数，本文讨论了三种常用的校准算法并利用模拟参数实验对其校准效果进行了检验。实验结果表明，Levenberg-Marquardt算法能够最快地向真实参数收敛，并且在初始参数估计有较大偏差的情况下仍能做到较高精度的校准。因此在后续的研究中，本文使用Levenberg-Marquardt算法对含有参数的期权模型进行参数校准。由于本地波动率模型属于不含有参数的模型，其校准方法利用Dupire公式进行直接计算。在利用市场期权价格对模型进行校准后，本文对五种期权定价模型进行了避险有效性的实证检验，避险资产选为奇异期权中具有典型性的障碍期权和亚式期权，避险策略使用最小方差策略和Delta-vega中性策略。测试结果表明，模型的避险有效性与奇异期权的路径依赖性有显著的关联，随着路径依赖性增强，所有模型的避险有效性都有所减弱。在模型相对避险效果的比较中，结果表明在使用最小方差策略时，Bates模型的避险效果最佳；而在使用Delta-vega中性策略时，，Heston的随机波动率模型避险效果最佳。
[Abstract]:This paper selects the Hang Seng China Enterprise Index as the underlying asset of singular options to test the hedging effectiveness of the option pricing model. Black-Scholes model Merton's jump diffusion model and Heston's stochastic volatility model Bates model and local volatility model. The five popular models are selected as the representative of option pricing model. In order to estimate the model parameters, three common calibration algorithms are discussed and their calibration results are tested by simulated parameter experiments. The experimental results show that Levenberg-Marquardt algorithm can converge to real parameters as quickly as possible. And the accuracy of calibration can be achieved even if the initial parameter estimation has a large deviation. Therefore, in the subsequent research, In this paper, Levenberg-Marquardt algorithm is used to calibrate the option model with parameters. Because the local volatility model belongs to the model without parameters, its calibration method is directly calculated by Dupire formula. After calibrating the model by using the market option price, this paper makes an empirical test on the hedging effectiveness of the five options pricing models. The hedge assets are selected as the typical barrier options and Asian options in the singular options. The minimum variance strategy and Delta-vega neutral strategy are used in the hedging strategy. The test results show that the hedging effectiveness of the model is significantly related to the path dependence of the singular options, and with the increase of the path dependence, The results show that the Bates model has the best hedge effect when the minimum variance strategy is used. When using Delta-vega neutral strategy, the stochastic volatility model of Delta-vega is the best to avoid risk.
【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

【相似文献】