發(fā)布時(shí)間：2017-07-28 08:01

Abstract

我們將專(zhuān)注于在離散時(shí)間內(nèi)以交易成本進(jìn)行復(fù)制。 為了做到這一點(diǎn)，，我們將以交易成本對(duì)選項(xiàng)復(fù)制進(jìn)行系統(tǒng)審查。 期權(quán)復(fù)制模型基于Cox-Ross-Rubinstein二項(xiàng)期權(quán)定價(jià)模型。 本文將對(duì)Boyle和Vorst的長(zhǎng)期和短期期權(quán)方案進(jìn)行離散時(shí)間法的研究，并對(duì)數(shù)值改變各種參數(shù)的影響進(jìn)行調(diào)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目錄
1.介紹1
2.文學(xué)評(píng)論3
2.1概述3
2.2具有交易成本的期權(quán)定價(jià)的Black-Scholes模型4
2.3 Black-Scholes模型的期權(quán)定價(jià)與投資組合6
3.Methodology8
3.1關(guān)于期權(quán)定價(jià)的Black-Scholes模型8
3.2離散時(shí)間9
3.3 Leland方法11
3.4 Boyle -Vorst方法14
3.4.1具有交易成本的離散時(shí)間選項(xiàng)復(fù)制14
3.4.2復(fù)印組合作為折現(xiàn)期望16
3.4.3短信期權(quán)價(jià)格18
數(shù)值計(jì)算20
4.1歐洲長(zhǎng)途電話(huà)不同連續(xù)利率的比較21
4.2歐洲長(zhǎng)途電話(huà)不同修訂次數(shù)的比較24
4.3歐洲長(zhǎng)途電話(huà)不同標(biāo)準(zhǔn)差的比較25
4.4 Black-Scholes近似值和Leland近期長(zhǎng)期看漲期權(quán)價(jià)格27
4.5歐洲短期通話(huà)價(jià)格比較29
5結(jié)論32
6附錄33
7參考文獻(xiàn)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介紹

愛(ài)因斯坦和維納在1905年提出的函數(shù)功能的重要性質(zhì)。使用布朗運(yùn)動(dòng)，Bachelier（1900）具體描述了股票價(jià)格的變化，并提供了歐式看漲期權(quán)的公式。 Black＆Scholes（1973）提出了著名的Black-Scholes模型。此外，Merton（1973）在許多方面系統(tǒng)地研制了Black-Scholes模型和定價(jià)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. Moreorevision times increase, the option price will slightly increase. With the fixed number of revision time, when the riskless continuous interest rate increases, the option price will significantly increase. By comparing the different standard deviation of the European long call price, with fixed transaction cost rate on stocks, when the number of revision time increases, the option price will slightly decrease. Moreover, there is positive relationship between the volatility of the risky asset (standard deviation) and option price. 
By comparing the European short call price, the transaction cost rate on stocks k can negatively affect the option price. Moreover, there is negative relationship between option price and the riskless continuous interest rates. There is significant difference between the option price without transaction costs and the option price with transaction costs. Both the Black Scholes approximation and Leland’s approximation can get accurate value of option price. On the other hand, when there are transaction costs, there is no significant difference between the Black Scholes approximation and the Leland’s approximation. 

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