二叉树模型与基于B-S模型的随机波动率下期权模型定价效率的实证检验

发布时间：2018-03-19 13:14

本文选题：二叉树期权定价模型　切入点：随机波动率模型　出处：《东北财经大学》2012年硕士论文　论文类型：学位论文

【摘要】：随着世界经济的一体化,金融衍生产品市场的环境和条件的日臻成熟,期权定价理论也在逐步完善,对金融交易、公司财务管理、风险管理中起到重要的指导作用。各种衍生品的定价原理基本上可以分为秩方法、偏微分方程方法、动态规划法,蒙特卡罗模拟法。关于期权定价,最著名和适用最广泛的方法有两种。一种是动态规划法中的二项式期权定价模型(The Binomial Option Pricing Model, BOPM),又称“二叉树”期权定价模型,其理论要点最初见诸于John C.Cox、S.A.Ross以及Mark Rubinstein于1979年所著的一篇论文之中。另一种是偏微分方程法中的Black-Scholes期权定价模型(The Black-Scholes Option Pricing Model, BSOPM)。B-S公式在实际中得到了大量应用,但是,B-S公式中存在大量不符合实际金融、经济的假设前提,使得B-S公式在实际应用中不能完美解释市场中的实际情况。弱化B-S公式中不合市场实际的假设,对B-S模型进行改进,总的来看主要是基于标的资产的价格服从对数正态分布,波动率为常数两个方面进行的。Bates(1966)随机波动率-随机跳跃模型结合了Merton(1976)的跳跃-扩散模型和Heston(1993)的随机波动率模型,同时考虑了加入随机跳跃和随机波动率两个方面。本文在阐述国外成熟期权定价理论基础上,以我国之前存在的权证市场,用二叉树模型、B-S模型、SVJ模型,试着对我国的权证产品进行定价,试图从理论上分析这几种模型对我国权证产品的定价效率,通过实验验证寻找对B-S模型定价的有效改进和适合国内市场的期权定价模型。实验结果表明：在B-S模型基础上,考虑随机波动率后的SVJ模型对权证的定价效率最高,虽然在权证后期存在较大的低估现象,但是相比较于离散的二叉树模型和基础的B-S期权定价模型,在对期权定价的拟合上,SVJ模型仍有相对较大的优势。
[Abstract]:With the integration of the world economy and the maturation of the environment and conditions of the financial derivatives market, the option pricing theory has been gradually perfected. The pricing principle of various derivatives can be divided into rank method, partial differential equation method, dynamic programming method, Monte Carlo simulation method. There are two most famous and widely used methods. One is the binomial option pricing model in dynamic programming and the Binomial Option Pricing Model, also known as "binomial tree" option pricing model. The main points of its theory were first found in a paper written by John C. Coxen S.A. Ross and Mark Rubinstein in 1979. The other is the Black-Scholes option pricing model in partial differential equation method and the Black-Scholes Option Pricing Model. BSOPM).B-S formula has been widely used in practice. However, there are a large number of assumptions in B-S formula that are not in line with the actual financial and economic conditions, which make the B-S formula not be able to explain the actual situation in the market perfectly in practical application, so as to weaken the assumption that the B-S formula is not practical in the market, and improve the B-S model. Generally speaking, it is mainly based on the logarithmic normal distribution and constant volatility of the underlying assets. At the same time, two aspects of random jump and random volatility are considered. On the basis of expounding the mature option pricing theory in foreign countries, this paper tries to price the warrant products in our country by using the binomial tree model and B-S model and SVJ model, based on the existing warrants market in China. This paper attempts to theoretically analyze the pricing efficiency of these models to warrant products in China, and find out the effective improvement of B-S model and the option pricing model suitable for the domestic market through the experimental verification. The experimental results show that, on the basis of B-S model, the SVJ model with random volatility has the highest pricing efficiency for warrants, although there is a large underestimation phenomenon in the latter stage of warrants. However, compared with the discrete binary tree model and the basic B-S option pricing model, SVJ model still has a relatively large advantage in the fitting of option pricing.
【学位授予单位】：东北财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830;F224

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