Abstract
我们将专注于在离散时间内以交易成本进行复制。 为了做到这一点，我们将以交易成本对选项复制进行系统审查。 期权复制模型基于Cox-Ross-Rubinstein二项期权定价模型。 本文将对Boyle和Vorst的长期和短期期权方案进行离散时间法的研究，并对数值改变各种参数的影响进行调查研究。We will be focusing on the option replication in discrete time with transaction costs. To do this we will review systematically on the option replication with transaction costs. The model on option replication is based on the Cox-Ross-Rubinstein binomial option pricing model. The paper willimplement the discrete-time method of Boyle and Vorst for long and short call optionprices, and investigate numerically the effect of changing thevarious parameters.
Table of Contents目录
1.介绍1
2.文学评论3
2.1概述3
2.2具有交易成本的期权定价的Black-Scholes模型4
2.3 Black-Scholes模型的期权定价与投资组合6
3.Methodology8
3.1关于期权定价的Black-Scholes模型8
3.2离散时间9
3.3 Leland方法11
3.4 Boyle -Vorst方法14
3.4.1具有交易成本的离散时间选项复制14
3.4.2复印组合作为折现期望16
3.4.3短信期权价格18
数值计算20
4.1欧洲长途电话不同连续利率的比较21
4.2欧洲长途电话不同修订次数的比较24
4.3欧洲长途电话不同标准差的比较25
4.4 Black-Scholes近似值和Leland近期长期看涨期权价格27
4.5欧洲短期通话价格比较29
5结论32
6附录33
7参考文献35
1. Introduction 1
2. Literature review 3
2.1 Overview 3
2.2 Black-Scholes model on option pricing with Transaction Costs 4
2.3 Black-Scholes model on option pricing with investment portfolio 6
3.Methodology 8
3.1 Black-Scholes model on option pricing 8
3.2 Discrete time 9
3.3 Leland method 11
3.4 Boyle –Vorst method 14
3.4.1 Option Replication in Discrete Time with Transaction Costs 14
3.4.2The Replicating Portfolio as a Discounted Expectation 16
3.4.3The Short Call Option price 18
4. Numerical Calculations 20
4.1 Comparison of different continuous interest rate of the European long call price 21
4.2 Comparison of different number of revision times of the European long call price 24
4.3 Comparison of different standard deviation of the European long call price 25
4.4 The Black-Scholes approximation and Leland’s approximation for long call option price 27
4.5 Comparison of the European short call price 29
5 Conclusions 32
6 Appendix 33
7 References 35
1. Introduction介绍
爱因斯坦和维纳在1905年提出的函数功能的重要性质。使用布朗运动，Bachelier（1900）具体描述了股票价格的变化，并提供了欧式看涨期权的公式。 Black＆Scholes（1973）提出了着名的Black-Scholes模型。此外，Merton（1973）在许多方面系统地研制了Black-Scholes模型和定价公式。 The history of option price should back to the French mathematician Louis Bachelier in 1900. He has realized some important properties of Wiener function proposed by Einstein and Wiener in 1905. Using the Brownian motion, Bachelier (1900)has specifically described the change of stock price and provided the formula of European call option. Black &Scholes (1973) proposed the famous Black-Scholes model. Moreover, Merton (1973) systematically developed the Black-Scholes model and pricing formula in many aspects. In 1976, Cox &Ross (1976) proposed the risk-neutral pricing theory. Furthermore, Cox, Ross and Rubinstein (1979) simplified the proof of the Black-Scholes model by using fundamental theorem of asset pricing and proposed the multiplicative binomial lattice option pricing model. Many scholars have focused on this issue in the following years. Using the continuous-time framework, Leland (1985) studied the option price of proportional transaction costs. The replicating stock-bond portfolio constructed by Leland (1985) can be used to replicate the option at maturity. Merton (1990) researched the Black-Scholes model on the discrete-time framework. By using the risky asset portfolio and the riskless bonds, Merton (1990) can accurately replicate the option value at expiration. Boyle&Vorst (1992) extended the option pricing model of Merton (1990) to a discrete-time framework. Moreover, they proposed an asset portfolio which can replicate the European long call price and the European short call price.
Options began trading on the Chicago Board Options Exchange in 1973. In the following decades, options bring great impact and influence on financial theory. Nowadays, the options market has become an important component of international financial markets. As the pricing system of financial derivatives have important effects on market
