本文選題：二叉樹期權(quán)定價(jià)模型　切入點(diǎn)：隨機(jī)波動(dòng)率模型　出處：《東北財(cái)經(jīng)大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著世界經(jīng)濟(jì)的一體化,金融衍生產(chǎn)品市場的環(huán)境和條件的日臻成熟,期權(quán)定價(jià)理論也在逐步完善,對金融交易、公司財(cái)務(wù)管理、風(fēng)險(xiǎn)管理中起到重要的指導(dǎo)作用。各種衍生品的定價(jià)原理基本上可以分為秩方法、偏微分方程方法、動(dòng)態(tài)規(guī)劃法,蒙特卡羅模擬法。關(guān)于期權(quán)定價(jià),最著名和適用最廣泛的方法有兩種。一種是動(dòng)態(tài)規(guī)劃法中的二項(xiàng)式期權(quán)定價(jià)模型(The Binomial Option Pricing Model, BOPM),又稱“二叉樹”期權(quán)定價(jià)模型,其理論要點(diǎn)最初見諸于John C.Cox、S.A.Ross以及Mark Rubinstein于1979年所著的一篇論文之中。另一種是偏微分方程法中的Black-Scholes期權(quán)定價(jià)模型(The Black-Scholes Option Pricing Model, BSOPM)。B-S公式在實(shí)際中得到了大量應(yīng)用,但是,B-S公式中存在大量不符合實(shí)際金融、經(jīng)濟(jì)的假設(shè)前提,使得B-S公式在實(shí)際應(yīng)用中不能完美解釋市場中的實(shí)際情況。弱化B-S公式中不合市場實(shí)際的假設(shè),對B-S模型進(jìn)行改進(jìn),總的來看主要是基于標(biāo)的資產(chǎn)的價(jià)格服從對數(shù)正態(tài)分布,波動(dòng)率為常數(shù)兩個(gè)方面進(jìn)行的。Bates(1966)隨機(jī)波動(dòng)率-隨機(jī)跳躍模型結(jié)合了Merton(1976)的跳躍-擴(kuò)散模型和Heston(1993)的隨機(jī)波動(dòng)率模型,同時(shí)考慮了加入隨機(jī)跳躍和隨機(jī)波動(dòng)率兩個(gè)方面。 本文在闡述國外成熟期權(quán)定價(jià)理論基礎(chǔ)上,以我國之前存在的權(quán)證市場,用二叉樹模型、B-S模型、SVJ模型,試著對我國的權(quán)證產(chǎn)品進(jìn)行定價(jià),試圖從理論上分析這幾種模型對我國權(quán)證產(chǎn)品的定價(jià)效率,通過實(shí)驗(yàn)驗(yàn)證尋找對B-S模型定價(jià)的有效改進(jìn)和適合國內(nèi)市場的期權(quán)定價(jià)模型。 實(shí)驗(yàn)結(jié)果表明：在B-S模型基礎(chǔ)上,考慮隨機(jī)波動(dòng)率后的SVJ模型對權(quán)證的定價(jià)效率最高,雖然在權(quán)證后期存在較大的低估現(xiàn)象,但是相比較于離散的二叉樹模型和基礎(chǔ)的B-S期權(quán)定價(jià)模型,在對期權(quán)定價(jià)的擬合上,SVJ模型仍有相對較大的優(yōu)勢。
[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.
【學(xué)位授予單位】：東北財(cái)經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F830;F224

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本文編號：1634417