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Stock price follows the mixing process option pricing model

Author: WangQiMing
Tutor: LiuXinPing
School: Shaanxi Normal University
Course: Applied Mathematics
Keywords: Option Pricing Black-Scholes model Mixing process Bonus
CLC: F830.91
Type: Master's thesis
Year: 2008
Downloads: 159
Quote: 0
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Abstract


This thesis work and innovation: to use saddle theory, stochastic analysis and mathematical tools native options assets (stock) price behavior analysis, and simulation of the real trend of the stock price, stock price constructed obey two new models of the mixing process, the establishment of a mathematical model of option pricing, and the pricing formula is derived. This paper is divided into four chapters: the first chapter is an introduction, a brief introduction of the formation mechanism of the option value of option pricing theory meaning, origin, development, and dynamic. The second chapter assumes that the stock price on the basis of analysis of the main factors of the option price, to meet geometric Brownian motion and other conditions, the use of no-arbitrage principle and Ito formula introduced the famous Black-Scholes model. Expounded in detail the derivation of stock price follows a BS partial differential equations, and the BS pricing formula introduced by the BS equation, and analyzes the deficiency of the pricing formula. Chapter description of the stochastic process of the stock price movement, and summarized several random process often used in the study of option pricing, parse and compare various models through the random nature of the digital features contrast Describe reasonable and shortcomings of the stock price movement. Chapter on the basis of the analysis in the third chapter of the stock price behavior patterns, the introduction of a new model of the stock price movement of the two simulations. One Ito process and pulse interference process is superimposed, the establishment of a new mixing process of the stock price follows the jump - diffusion process. By changing the assumptions of the model of stock price behavior, the stock price follows the Ito the process and pulse interference process mixed distribution of European option pricing model, the stochastic differential equation satisfied by the stock price: and on this basis, discussed why he did not dividends payable and payment bonus European option pricing formula undetermined. Another model is the basis of the assumption that the classic stock prices follow Ito processes, adding Markov jump process, both a new composite mixing process. Stock prices by changing the assumptions of the model of stock price behavior, obey Ito process and Markov jump process mixed distribution of European option pricing model, the stochastic differential equation satisfied by the stock price: and discussed why he did not on the basis of dividends payable European pay dividends undecided option pricing formula. The two types of mixing process is described the native normal asset price fluctuations caused by economic factors, more accurately described bring the native asset prices jump by an unusual non-economic factors. Therefore, assuming that the native asset prices obey the mixing process is an ideal choice.

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CLC: > Economic > Fiscal, monetary > Finance, banking > Finance, banking theory > Financial market > Securities market
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