期权做市商波动率管理：隐含波动率曲面建模与预测

发布时间：2018-04-26 17:37

本文选题：期权做市商 + 动态隐含波动率　；参考：《浙江大学》2016年博士论文

【摘要】：期权在金融市场中占据重要地位,从国际经验来看,期权和期货、现货作为场内市场的基础产品,互相配合,构建起较为完整的场内风险管理体系。2015年2月9日,上证50ETF期权正式上线,研究期权定价及其相关问题对我国金融市场的发展与完善有重要意义。我国期权市场处于发展的初期,虽然前期准备工作丰富,但是,加强从业人员理论与业务水平、进一步深入投资者教育任重道远。写这篇博士论文的目的并不仅仅在于总结本人博士期间的研究成果,而是希望对波动率曲面建模的发展历程做一个系统性的总结,为致力于促进衍生品市场发展或对衍生品交易感兴趣的各界人士提供一个理论参考。波动率曲面是研究衍生品定价、交易和风险控制的重中之重,一方面,通过Black-Scholes公式它与期权报价有一一对应的关系,被业界工作者广泛的用于衡量期权价格水平；另一方面,它是建立场内衍生品和场外衍生品关系的桥梁。每个模型的初衷是什么?为什么要做这样的假设或改进?模型存在哪些优点与不足?这都是本文要考察的问题。Black-Scholes模型奠定了现代期权定价理论的基石,它促进了期权市场及衍生品定价理论的发展。然而Black-Scholes模型的常数隐含波动率假设与市场上实际观测到的“隐含波动率曲面”现象不符,促使后续研究者们寻找能更合理刻画隐含波动率曲面现象的模型,如随机波动率模型、跳扩散模型、局部波动率模型等。诸多经验研究表明,隐含波动率会随时间动态变化,这些模型的参数不稳定,在描述隐含波动率曲面的动态变化上有缺陷,为与动态波隐含动率模型区分,我们称之为“静态隐含波动率模型”。为描述隐含波动率随时间变化的动态特征,一些学者提出了“动态隐含波动率模型”,直接对隐含波动率动态进行建模,力图在拟合隐含波动率曲面在某一时刻的形态的同时,刻画隐含波动率曲面随着时间的变化规律。隐含波动率曲面是研究期权定价、风险管理以及交易策略的核心,同时也是连接场内衍生品市场与场外衍生品市场的媒介。从场内做市商的角度来看,模型的定价误差越小越好,模型价格最好能在市场买卖价差的范围之内,因为做市商要跟随市场观点、很少违背市场。从场外衍生品的定价和对冲角度来看,定价模型应尽量精确的拟合场内期权波动率曲面,使得场内衍生品和场外衍生品在统一的框架下定价,避免套利机会的形成。本文从场内期权做市商的角度,研究期权隐含波动率曲面的构建问题。本文所做的工作主要有：1.总结了构建隐含波动率曲面的五大类方法,通过对比不同模型的拟合精度、计算速度、理论背景、参数稳定度,分析使用不同模型作为做市商插值模型刻画单一时刻隐含波动率曲面的合理性。2.详细阐述了构建波动率曲面时涉及的实际问题与解决方案；改进SABR模型、SVI参数化形式的参数优化过程,提高计算速度和模型参数的稳定性。在黄金ETF期权日内交易数据上测试了SABR模型和SVI模型的参数稳定性,说明了构建动态隐含波动率模型的必要性。3.深入研究动态隐含波动率模型,介绍了现存的三种隐含波动率曲面动态建模方法,并分析了他们的缺陷,包括：基于市场的(market-based)动态隐含波动率模型、Vega-Gamma-Vanna-Volga模型、基于因子的(factor-based)动态隐含波动率模型。本文提出了一般化动态隐含波动率因子模型,可用于刻画整个波动率曲线或曲面的动态。并引入无损卡尔曼滤波(unscented Kalman filter)解决了非线性系统的优化问题,提供了估计模型参数和预测未来隐含波动率曲面的有效方法。4.用标准普尔500指数期权隐含波动率日内数据做实证分析,检测了一般化动态隐含波动率因子模型的参数估计和预测效果；对比了静态模型、其他动态隐含波动率模型；验证了基于因子的一般化动态隐含波动率模型的理论和实证意义。
[Abstract]:Option plays an important role in the financial market. From the international experience, options and futures, spot as the base products of the field market, cooperate with each other to build a more integrated field risk management system in February 9th.2015, Shanghai Stock 50ETF option is formally launched, and research options pricing and related issues to the development of China's financial market and the development of the financial market It is of great significance. The option market in China is in the early stage of development. Although the preparatory work is rich in the early period, it is very difficult to strengthen the theory and business level of the practitioners and further deepen the education of investors. The purpose of writing this doctoral thesis is not only to summarize the research results of my blogger but to the volatility. A systematic summary of the development process of surface modeling is made to provide a theoretical reference for people of all walks of life who are interested in promoting the development of derivatives market or for derivatives trading. Volatility surface is the most important factor in the study of derivatives pricing, transaction and risk control. On the one hand, it has a Black-Scholes formula with the option price. One corresponding relationship is widely used by industry workers to measure the price level of options; on the other hand, it is a bridge to establish the relationship between field derivatives and OTC derivatives. What is the original intention of each model? Why do you want to make such a hypothesis or improvement? What are the advantages and disadvantages of the model? This is the question.Black-S The choles model establishes the cornerstone of the modern option pricing theory, which promotes the development of the option market and derivatives pricing theory. However, the constant implied volatility hypothesis of the Black-Scholes model is inconsistent with the "implied volatility surface" observed in the market, prompting the follow-up researchers to find a more reasonable description of the implied volatility. The model of rate surface phenomena, such as random wave rate model, jump diffusion model, local wave rate model, and so on. Many empirical studies show that the implied volatility will change dynamically with time, the parameters of these models are unstable, and the dynamic changes in the implied wave rate surface have a lack of subsidence, which is distinguished from the dynamic wave implicit dynamic model. In order to describe the dynamic characteristics of the implied volatility, some scholars have proposed a dynamic implicit volatility model to model the implicit volatility dynamics directly, and try to describe the implicit wave rate surface with time while the implicit wave rate surface is in the form of a certain time. The implicit volatility surface is the core of the option pricing, risk management and trading strategy, and it is also the medium to connect the market in the field and the OTC derivatives market. From the point of view of the market maker, the smaller the pricing error, the better the model price can be within the range of the market price difference. Because the market makers should follow the market view and rarely violate the market. From the point of view of the pricing and hedging of the OTC derivatives, the pricing model should be as accurate as possible to fit the volatility surface of the options, making the field derivatives and over-the-counter derivatives priced in a unified framework and avoiding the formation of the opportunity for the hedging. To study the construction of implied volatility surface of options. The main work of this paper is as follows: 1. the five kinds of methods for constructing implicit volatility surface are summarized. By comparing the fitting accuracy of different models, the calculation speed, the theoretical background, the parameter stability, and the analysis and use of different models as the market maker interpolation model, the single time is described. The rationality of implied volatility surface.2. elaborated the actual problems and solutions involved in the construction of wave rate surface, improved the parameter optimization process of SABR model, SVI parameterization, improved the calculation speed and the stability of the model parameters. The parameter stability of the SABR model and SVI model was tested on the day of transaction number of gold ETF option. Qualitatively, the necessity of Constructing Dynamic Implicit volatility model (.3.) is described in depth and the Dynamic Implicit volatility model is deeply studied. Three existing dynamic modeling methods of implicit volatility surface are introduced, and their defects are analyzed, including the market based (market-based) Dynamic Implicit volatility model, Vega-Gamma-Vanna-Volga model, and based on the market. The Dynamic Implicit volatility model of factor (factor-based). This paper presents a general dynamic implicit volatility factor model, which can be used to describe the dynamics of the whole wave rate curve or surface, and introduces the nondestructive Calman filter (unscented Kalman filter) to solve the optimization problem of nonlinear systems, and provides the estimation model parameters and prediction. The effective method to imply the volatility surface is an empirical analysis of the implicit volatility of the standard & Poor's 500 index option. The parameter estimation and prediction effect of the general dynamic implicit volatility factor model is detected, and the static model and other dynamic implicit volatility models are compared. The general dynamic implicit method based on the factor is verified. The theoretical and empirical significance of the volatility model.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F830.91;F224

【参考文献】