本文關(guān)鍵詞： 仿射跳擴(kuò)散過(guò)程 自下而上的方法 帶移民的分支過(guò)程 抵押債務(wù)憑證 抵押債務(wù)憑證分券 信用違約掉期 信用風(fēng)險(xiǎn) 對(duì)手風(fēng)險(xiǎn) 信用溢價(jià) 違約相關(guān) 雙隨機(jī) Poisson 過(guò)程 動(dòng)態(tài)對(duì)沖 流動(dòng)風(fēng)險(xiǎn) 組合信用衍生品 隨機(jī)中心回歸 結(jié)構(gòu)化模　出處：《南開(kāi)大學(xué)》2012年博士論文　論文類型：學(xué)位論文

【摘要】：這篇博士論文研究了幾個(gè)不確定條件下的衍生品定價(jià)問(wèn)題.我們主要考慮了三類衍生品:第一類是組合信用衍生品(多標(biāo)的信用衍生品),主要考慮抵押債務(wù)憑證(CDO)以及n次違約CDS;第二類是公司債券,公司債券可以看作是公司價(jià)值的信用衍生品;第三類是波動(dòng)率互換,考慮了其最優(yōu)動(dòng)態(tài)對(duì)沖問(wèn)題. 組合信用衍生品是近十年來(lái)迅速發(fā)展的一類信用衍生品,通常用來(lái)轉(zhuǎn)移組合信用風(fēng)險(xiǎn).與其它常見(jiàn)的信用衍生品(如信用違約掉期)相比,組合信用衍生品的標(biāo)的資產(chǎn)是一個(gè)資產(chǎn)池,其現(xiàn)金流則取決于這個(gè)資產(chǎn)池中資產(chǎn)的損失(違約)情況.組合信用風(fēng)險(xiǎn)建模的困難是資產(chǎn)池中資產(chǎn)的數(shù)目太多,靈活的模型往往需要借助Monte Carlo模擬來(lái)進(jìn)行衍生品定價(jià)和模型校準(zhǔn),時(shí)間花費(fèi)巨大.本論文的第二章和第三章致力于建立計(jì)算簡(jiǎn)便又具有相應(yīng)靈活性的組合信用風(fēng)險(xiǎn)模型,分別從自下而上和自上而下兩個(gè)角度考慮了組合信用衍生品的定價(jià)問(wèn)題. 第二章從自下而上的角度給出了兩類組合信用風(fēng)險(xiǎn).第一類利用[1]提出的模型,我們給出了一個(gè)計(jì)算組合信用衍生品的新方法,該方法在計(jì)算衍生品價(jià)格時(shí)不依賴于Fourier變換以及Fourier逆變換,也無(wú)需使用Monte Carlo模擬.我們的第二類模型不同于[1],但仍能利用仿射跳擴(kuò)散過(guò)程以及雙隨機(jī)Poisson過(guò)程的信用風(fēng)險(xiǎn)模型,使得該模型易于計(jì)算.我們給出了公司債券,信用違約掉期以及組合信用衍生品的定價(jià)方法. 第三章從自上而下的角度考慮組合信用風(fēng)險(xiǎn).我們首先利用帶移民的離散時(shí)間分支過(guò)程對(duì)資產(chǎn)池中違約資產(chǎn)的個(gè)數(shù)進(jìn)行建模,在違約回復(fù)率是常數(shù)的前提下得到了抵押債務(wù)憑證的定價(jià)方法.我們進(jìn)行了數(shù)值試驗(yàn)來(lái)研究不同參數(shù)對(duì)價(jià)格的影響,結(jié)果表明我們的模型具有相應(yīng)的靈活性,能夠刻畫(huà)市場(chǎng)價(jià)格的變動(dòng).此模型的缺點(diǎn)是違約資產(chǎn)的個(gè)數(shù)可能會(huì)遠(yuǎn)大過(guò)資產(chǎn)池中資產(chǎn)的總數(shù).特別是當(dāng)資產(chǎn)總數(shù)較少時(shí)定價(jià)可能會(huì)不準(zhǔn)確.因此我們進(jìn)一步提出了一個(gè)改進(jìn)的模型,通過(guò)設(shè)立一個(gè)“對(duì)照資產(chǎn)池”,并對(duì)“對(duì)照資產(chǎn)池”中違約資產(chǎn)個(gè)數(shù)進(jìn)行建模,解決了“原資產(chǎn)池”中違約資產(chǎn)個(gè)數(shù)可能遠(yuǎn)大過(guò)資產(chǎn)總數(shù)的問(wèn)題. 在第四章,我們將注意力集中到流動(dòng)性風(fēng)險(xiǎn)對(duì)公司債券價(jià)格的影響方面.通過(guò)結(jié)構(gòu)化方法建立債券價(jià)格模型,并引入流動(dòng)性風(fēng)險(xiǎn),我們得到了公司債券價(jià)格的解析表達(dá)式.數(shù)值試驗(yàn)的結(jié)果表明在該模型下,公司債券短期的期限結(jié)構(gòu)發(fā)生了變化,產(chǎn)生了風(fēng)險(xiǎn)溢價(jià),從而解決了在一般的結(jié)構(gòu)化模型中(比如[2])公司債券的短期風(fēng)險(xiǎn)溢價(jià)為零的問(wèn)題. 在第五章,我們考慮波動(dòng)率互換的對(duì)沖問(wèn)題.假設(shè)標(biāo)的資產(chǎn)的價(jià)格動(dòng)態(tài)分別服從離散時(shí)間和連續(xù)時(shí)間下的平穩(wěn)獨(dú)立增量過(guò)程,我們得到了相應(yīng)的動(dòng)態(tài)最優(yōu)對(duì)沖策略.我們以[3]中的跳擴(kuò)散過(guò)程為例進(jìn)行了數(shù)值試驗(yàn),結(jié)果顯示對(duì)沖誤差達(dá)到了0.5%以內(nèi).
[Abstract]:This doctoral thesis studies the pricing of derivatives under several uncertain conditions. We mainly consider three types of derivatives: the first is portfolio credit derivatives (multi-subject credit derivatives). The main consideration is CDO (CDO) and default CDSs (n times); The second is corporate bonds, which can be regarded as credit derivatives of corporate value; The third is volatility swap, which considers its optimal dynamic hedging problem. Portfolio credit derivatives are a kind of credit derivatives developed rapidly in the past decade, which are usually used to transfer portfolio credit risk, compared with other common credit derivatives (such as credit default swaps). The underlying assets of portfolio credit derivatives are a pool of assets whose cash flow depends on the loss (default) of the assets in the pool. The difficulty of modeling portfolio credit risk is that there are too many assets in the pool of assets. Flexible models often require Monte Carlo simulations to price derivatives and calibrate models. The second and third chapters of this paper are devoted to the establishment of a simple and flexible portfolio credit risk model. The pricing of portfolio credit derivatives is considered from the bottom-up and top-down perspectives respectively. In the second chapter, two types of combination credit risk are given from the bottom-up perspective. [In the proposed model, we present a new method for calculating portfolio credit derivatives, which does not depend on Fourier transform and Fourier inverse transformation in calculating the price of derivatives. There is no need to use Monte Carlo simulation. Our second model is different from. [1], but the credit risk model of affine jump diffusion process and double stochastic Poisson process can still be used to make the model easy to calculate. We give the corporate bond. The pricing of credit default swaps and portfolio credit derivatives. In the third chapter, we consider portfolio credit risk from a top-down perspective. Firstly, we use the discrete time branching process with immigration to model the number of defaulted assets in the asset pool. Under the condition that default response rate is constant, the pricing method of CDOs is obtained. We have carried out numerical experiments to study the effect of different parameters on the price. The results show that our model has the corresponding flexibility. The disadvantage of this model is that the number of defaulted assets may be larger than the total number of assets in the asset pool. Especially when the total number of assets is small, pricing may not be accurate. An improved model has been developed. By setting up a "controlled asset pool" and modeling the number of defaulted assets in the "controlled asset pool", the problem that the number of defaulted assets in the "original asset pool" may exceed the total number of assets is solved. In Chapter 4th, we focus on the influence of liquidity risk on corporate bond price. Through structured approach, we establish bond price model and introduce liquidity risk. We obtain the analytical expression of the corporate bond price. The numerical results show that the short-term maturity structure of corporate bonds has changed under the model, resulting in a risk premium. Thus solving the problem in general structured models such as [(2) the problem of zero short-term risk premium for corporate bonds. In Chapter 5th, we consider the hedging problem of volatility swaps. We assume that the price dynamics of underlying assets are based on the stationary independent increment process of discrete time and continuous time respectively. We get the corresponding dynamic optimal hedging strategy. We use the [The numerical results show that the hedge error is less than 0.5%.
【學(xué)位授予單位】：南開(kāi)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2012
【分類號(hào)】：F830.9;F224

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