考虑跳风险价值的欧式脆弱期权定价

发布时间：2018-04-10 14:12

本文选题：脆弱期权定价 + 违约风险　；参考：《中国矿业大学》2017年硕士论文

【摘要】：信用风险是金融市场中的一类难以被定量分析以及管理的风险。信用衍生产品自1992年被提出以来,以其现实中的实用性深受投资者追捧并获得了快速的发展。但是实际市场中的信用衍生品交易中,场外交易(OTC)份额占到了交易总额的绝大部分。场外市场中由于没有特定的监管机构,导致其遭受信用违约风险的可能性显著增大。当期权的多头被同时暴露在市场风险和信用风险这两种风险下时,这种期权被认为是脆弱期权。现实生活中,公司资产的报告通常是按季度给出,为了更加准确地刻画出实际市场中的期权写方资产,本文第三章给出了一种不完备信息条件下脆弱期权的定价模型。在标的股票价格和期权写方资产价格均服从跳扩散过程的假设下,得到了不完备信息下含有信用风险和跳风险的脆弱期权定价的解析公式。并通过数值实验比较了不完备信息下的脆弱期权定价模型与B-S模型、Merton跳扩散模型、Klein模型三个经典期权模型下的期权价值。从近年来马尔可夫体制转换模型的实际研究可知,马尔可夫体制转换模型在刻画宏观经济周期方面,如经济结构调整、商业周期循环以及市场经济体制改变等获得了良好的效果;而我们所研究的市场经济中的股票回报率、无风险利率、外汇汇率等都与经济周期和市场经济体制的变化有关;因此研究基于体制转换的期权定价问题更能符合实际市场的需求。由于在体制转换模型假设下的金融市场通常是不完备的,导致等价鞅测度不唯一,因此如何构造和选取等价鞅测度也是本文研究的重要内容。本文第四章中,我们在标的股票价格和期权写方资产价格满足马尔可夫调制的跳扩散模型假设的基础上,研究了考虑跳的市场风险价格的欧式脆弱期权定价问题。在现有的研究跳风险的期权定价中,跳风险被分为两类进行研究,一类是将跳风险作为系统性风险进行研究,能够被套期保值;一类是将跳风险作为非系统性风险进行研究,不能被套期保值。本章中我们将跳风险作为系统风险进行定价,可以被套期保值,因而在从原始测度到风险中性测度的转换过程中需要考虑到跳风险的定价。在此基础上,我们还研究了跳风险不被定价以及考虑相同跳模式下的期权定价;为了进一步研究跳的风险价值,我们还将跳风险分别存在于标的股票和期权写方资产以及同时存在时的期权价值进行比较分析。
[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.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9

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