本文選題：脆弱期權定價 + 違約風險�。� 參考：《中國礦業(yè)大學》2017年碩士論文

【摘要】：信用風險是金融市場中的一類難以被定量分析以及管理的風險。信用衍生產品自1992年被提出以來,以其現實中的實用性深受投資者追捧并獲得了快速的發(fā)展。但是實際市場中的信用衍生品交易中,場外交易(OTC)份額占到了交易總額的絕大部分。場外市場中由于沒有特定的監(jiān)管機構,導致其遭受信用違約風險的可能性顯著增大。當期權的多頭被同時暴露在市場風險和信用風險這兩種風險下時,這種期權被認為是脆弱期權。現實生活中,公司資產的報告通常是按季度給出,為了更加準確地刻畫出實際市場中的期權寫方資產,本文第三章給出了一種不完備信息條件下脆弱期權的定價模型。在標的股票價格和期權寫方資產價格均服從跳擴散過程的假設下,得到了不完備信息下含有信用風險和跳風險的脆弱期權定價的解析公式。并通過數值實驗比較了不完備信息下的脆弱期權定價模型與B-S模型、Merton跳擴散模型、Klein模型三個經典期權模型下的期權價值。從近年來馬爾可夫體制轉換模型的實際研究可知,馬爾可夫體制轉換模型在刻畫宏觀經濟周期方面,如經濟結構調整、商業(yè)周期循環(huán)以及市場經濟體制改變等獲得了良好的效果;而我們所研究的市場經濟中的股票回報率、無風險利率、外匯匯率等都與經濟周期和市場經濟體制的變化有關;因此研究基于體制轉換的期權定價問題更能符合實際市場的需求。由于在體制轉換模型假設下的金融市場通常是不完備的,導致等價鞅測度不唯一,因此如何構造和選取等價鞅測度也是本文研究的重要內容。本文第四章中,我們在標的股票價格和期權寫方資產價格滿足馬爾可夫調制的跳擴散模型假設的基礎上,研究了考慮跳的市場風險價格的歐式脆弱期權定價問題。在現有的研究跳風險的期權定價中,跳風險被分為兩類進行研究,一類是將跳風險作為系統(tǒng)性風險進行研究,能夠被套期保值;一類是將跳風險作為非系統(tǒng)性風險進行研究,不能被套期保值。本章中我們將跳風險作為系統(tǒng)風險進行定價,可以被套期保值,因而在從原始測度到風險中性測度的轉換過程中需要考慮到跳風險的定價。在此基礎上,我們還研究了跳風險不被定價以及考慮相同跳模式下的期權定價;為了進一步研究跳的風險價值,我們還將跳風險分別存在于標的股票和期權寫方資產以及同時存在時的期權價值進行比較分析。
[Abstract]:Credit risk is a kind of risk which is difficult to be quantitatively analyzed and managed in financial market.Credit derivatives have been developed rapidly by investors because of their practicability since they were put forward in 1992.But in the real market, OTC accounts for the vast majority of credit derivatives trading.The absence of a specific regulator in the OTC market has significantly increased the risk of credit default.When long options are exposed to both market risk and credit risk, this option is considered to be a weak option.In real life, the report of company assets is usually given quarterly. In order to more accurately depict the option writer's assets in the actual market, the third chapter of this paper gives a pricing model of fragile options under the condition of incomplete information.Under the assumption that both the underlying stock price and the asset price of the writer of the option are subject to the process of jump diffusion, an analytical formula for pricing fragile options with credit risk and jump risk under incomplete information is obtained.Through numerical experiments, we compare the value of options under three classical options models, namely the fragile option pricing model with incomplete information and the Merton jump diffusion model and the Klein model with B-S model.From the practical research of Markov system transformation model in recent years, we can see that Markov system transformation model is used to depict the macroeconomic cycle, such as the adjustment of economic structure.The circulation of business cycle and the change of market economy system have got good results, but the stock rate of return, risk-free interest rate, foreign exchange rate and so on are all related to the change of economic cycle and market economy system.Therefore, the study of option pricing based on institutional transformation can better meet the needs of the actual market.Because the financial market under the assumption of institutional transformation model is usually incomplete, the equivalent martingale measure is not unique, so how to construct and select the equivalent martingale measure is also an important content of this paper.In the fourth chapter, based on the assumption that the underlying stock price and the option writer's asset price satisfy the Markovian modulation jump diffusion model, we study the European fragile option pricing problem considering the jump market risk price.In the existing research on the option pricing of jump risk, jump risk is divided into two categories: one is to study jump risk as systemic risk, and the other is to study jump risk as non-systemic risk.Cannot be hedged.In this chapter, we price jump risk as systematic risk and can be hedged, so we need to consider the pricing of jump risk in the process of transition from original measure to risk neutral measure.On this basis, we also study the non-pricing of jump risk and the option pricing under the same jump mode.We also make a comparative analysis of the value of the jump risk in the underlying stock and option writer's assets and in the simultaneous existence of the option.
【學位授予單位】：中國礦業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F224;F830.9

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