本文選題：期權(quán)定價(jià)　切入點(diǎn)：隨機(jī)利率　出處：《哈爾濱工程大學(xué)》2012年碩士論文

【摘要】：本文主要討論基于隨機(jī)利率模型的歐式期權(quán)定價(jià)問(wèn)題，包括以下幾個(gè)方面的內(nèi)容：隨機(jī)分析和期權(quán)定價(jià)基本理論，基于無(wú)紅利支付股票的衍生證券所必須滿足的Black-Scholes方程的產(chǎn)生及其背景知識(shí)，利用偏微分方法和等價(jià)鞅測(cè)度法分別求解Black-Scholes公式，在特定隨機(jī)利率模型和一般隨機(jī)利率模型下對(duì)歐式期權(quán)定價(jià)進(jìn)行討論，以及在更加復(fù)雜的假設(shè)下，，推導(dǎo)隨機(jī)利率模型下支付紅利的帶跳的歐式期權(quán)的定價(jià)公式. 本文對(duì)期權(quán)定價(jià)的討論都是以股票作為標(biāo)的資產(chǎn)來(lái)說(shuō)明，對(duì)股票價(jià)格的行為模式進(jìn)行了詳細(xì)的闡述，并且在無(wú)套利框架下，通過(guò)構(gòu)造包含衍生證券和標(biāo)的股票的組合，利用偏微分方法和等價(jià)鞅測(cè)度法分別推導(dǎo)出符合衍生證券價(jià)格的Black-Scholes方程，總結(jié)性地給出了兩種方法的內(nèi)在聯(lián)系．本文著重點(diǎn)在于改進(jìn)Black-Scholes模型的固有假設(shè)條件，在一般隨機(jī)利率模型下，就利率與股票波動(dòng)源是否相關(guān)兩種情況，對(duì)原有的期權(quán)定價(jià)公式進(jìn)行延拓.本文最后還給出了基于隨機(jī)利率模型支付紅利的帶跳的歐式期權(quán)定價(jià)的解析解，從而進(jìn)一步拓展了Black-Scholes期權(quán)定價(jià)模型.
[Abstract]:This paper mainly discusses the European option pricing problem based on stochastic interest rate model, including the following aspects: stochastic analysis and the basic theory of option pricing, Based on the generation and background knowledge of Black-Scholes equation for derivative securities without dividend payment, the Black-Scholes formula is solved by using partial differential method and equivalent martingale measure method, respectively. This paper discusses the pricing of European options under the specific stochastic interest rate model and the general stochastic interest rate model, and under more complicated assumptions, deduces the pricing formula of the hopped European option with dividend under the stochastic interest rate model. In this paper, the discussion of option pricing is explained by taking stock as the underlying asset, and the behavior mode of stock price is explained in detail, and the combination of derivative securities and underlying stock is constructed under the framework of no arbitrage. By using the partial differential method and the equivalent martingale measure method, the Black-Scholes equation corresponding to the price of derivative securities is derived, and the intrinsic relations of the two methods are given. The emphasis of this paper is to improve the inherent assumptions of the Black-Scholes model. Under the general stochastic interest rate model, whether the interest rate is related to the source of stock volatility, In the end, the analytical solution of European option pricing with jump based on stochastic interest rate model is given, which further extends the Black-Scholes option pricing model.
【學(xué)位授予單位】：哈爾濱工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F224;F830.9

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