跳跃聚集市场中的场内场外期权定价研究

Pricing options fairly is one of the guarantees of the smooth development of option market. Previous studies about option pricing are mainly based on the assumption that the underlying assets follow geometric Brownian motions or more general exponential Lévy processes. However, recent empirical studies have shown that jumps are not only found in asset return and volatility, but these jumps are also clustered due to self-excitement and cross-excitement. Therefore, Lévy processes fail to describe the jumps because they have independent increments. Taking this into account, we apply Hawkes processes to construct asset price models for characterizing jump-clustering risk; these models are Hawkes jump diffusion process and stochastic volatility model with Hawkes-type jumps, and they will be validated by theoretical analysis and the financial data from foreign and domestic markets. Then we utilize equilibrium pricing theory and utility indifference pricing theory to evaluate exchange-traded options and OTC options, respectively. At last, models are compared with each other by numerical analysis and empirical study. This research builds novel option pricing models on the basis of the newly-found characteristic of jump-clustering with respect to asset return and its volatility. From a theoretical point of view, the research aims to improve option pricing method, and from a practical point of view, it is helpful for investors and regulators to make decisions.

对期权进行公允定价是期权市场健康发展的一个重要保障。以往的期权定价研究大都是建立在标的资产服从几何布朗运动或更一般的指数列维过程基础上。然而，近期的实证研究发现，资产价格收益率和波动率都存在跳跃，且跳跃因“自我刺激”和“交叉刺激”而具有聚集特征，但列维过程因具有独立增量性而不能刻画跳跃聚集性。鉴于此，本项目首先运用Hawkes过程建立能刻画跳跃聚集风险的资产价格模型——Hawkes跳跃扩散过程模型和带Hawkes跳跃的随机波动率模型，并通过理论分析和国内外金融市场实际数据论证所建模型的科学性和合理性；然后利用均衡定价理论和效用无差别定价理论分别对场内期权和场外期权进行定价；最后通过数值分析和实证研究对模型进行比较。本项目就资产价格新发现的跳跃聚集特征建立新的期权定价模型，理论上完善了原有的期权定价方法，实践中能为投资者和监管部门提供决策参考。

随着我国期权品种的不断丰富和场内场外期权市场的快速发展，对期权进行合理定价是期权市场健康发展的重要基础之一。近期实证研究发现，资产价格收益率和波动率都存在跳跃，且跳跃因“自我刺激”和“交叉刺激”而具有聚集特征，但传统定价模型通常难以刻画跳跃聚集性。本项目主要运用Hawkes过程建立能刻画跳跃聚集风险的资产价格模型，并用于对含交易对手风险的场外期权定价以及场外互换期权和国外股票期权进行理论定价；此外还用于对场内股指期权和VIX期权定价。理论研究发现，考虑资产价格跳跃聚集性会显著影响期权价值；实证研究发现，考虑跳跃聚集性的模型能显著提高场内期权的定价能力。本项目就资产价格新发现的跳跃聚集特征建立新的期权定价模型，理论上完善了原有的期权定价方法，实践中能为投资者和监管部门提供决策参考。