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            英国金融学硕士毕业论文:Financial risk management and risk measures: Por

            来源: www.koshiobi.com 作者:anne 发布时间:2019-07-04 论文字数:9989字
            论文编号: sb2019070410253627155 论文语言:- 论文类型:-
            Abstract摘要 摘要 风险管理包括以可接受的风险获得预期利润。风险价值(VaR)是一种利用标准统计技术来全面衡量市场风险的方法。RockafellarUryasev(2000)改进了VaR的度量,提出了条件风险价值
            Abstract摘要
            摘要
            风险管理包括以可接受的风险获得预期利润。风险价值(VaR)是一种利用标准统计技术来全面衡量市场风险的方法。Rockafellar&Uryasev(2000)改进了VaR的度量,提出了条件风险价值(CVAR),这是一种有效的投资组合优化方法。本文的目的是利用平均CVAR方法寻找美国股票市场的最优组合。本研究将利用三对基本的高斯偶、恐慌偶和偏T偶,利用蒙特卡罗方法进行场景模拟。然后,利用希腊人线性化损失分布公式,可以得到各股票情景模拟的损失,即,Risk management involves in obtaining an expected profit with an acceptable risk. Value at Risk (VaR) is a method that can use the standard statistical techniques to completely measure the market risk. Rockafellar&Uryasev (2000) improved the measurement of VaR, and proposed the Conditional Value at Risk (CVaR), which is an effective approach to optimize portfolios. In the dissertation, we aim at using Mean-CVaR method to find optimal portfolio of American stock market. This research will use three basic couples of Gaussian Couple, Panic Couple and Skewed t couple to make scenarios simulation by Monte Carlo method. After that, by using the formula of Greeks linearized loss distribution, we can get the loss for the scenarios simulation of each stocks, that is, 〖 L〗_(t+1)^Δ=-(C_s^BS Δ+C_S^BS S_t X_(t+1,1)+C_σ^BS X_(t+1,2)). 最后,本研究将探讨不同类型的连接词对CVAR中最优投资组合结构的影响。(2005年),cvar=Φ(ω)=min(y∈r^m)〖f_uβ(ω,α)〉。本研究的目的是将Fβ(ω,α)转化为最小值。利用辅助函数,将CVAR的优化问题简化为线性规划问题:
            Lastly, this research will examine the effect the different types of copulas have on the structure of optimal portfolios in CVaR.According to McNeil et al. (2005), CVaR=Φ(ω)=min┬(y∈R^m )?〖F_β (ω,α)〗. The objective of this research is translated to the minimum of F_β (ω,α). By using the auxiliary function, the optimization problem ofCVaR can be simplified as the linear programming problem: 
            利用AMPL软件对CVAR优化问题进行了研究,结果表明,CVAR的最大值在于1组的恐慌偶分布和3组的偏T偶分布?;谎灾?,CVAR与股票价格具有相同的方向。另外,最优组合的权重与最优组合密切相关,最优组合的权重与相关水平相对相关。Using the software of Ampl, the results of the optimization problem on CVaR shows that the highest value of CVAR lies in the Panic couple distribution of group 1 and the Skewed-t Couple distribution of group 3. In other words, the CVaR has the same direction with the stock price. Moreover, the couple selection is closely related to the optimal portfolio, and the weight of optimal portfolio is relatively related to the correlation level.
            Keywords: CVaR, Gaussian Couple, Panic Couple, Skewed t couple, Monte Carlo, Loss function, Optimization
             
            Table of contents
            Abstract 1
            1. Introduction 2
            1.1 Motivation 2
            1.2 Research question 3
            1.3 Structure arrangement 3
            2. Literature review 4
            3. Methodology 7
            3.1 Linearized Loss distribution 7
            3.2 Convexity function 8
            3.3 Couples and Simulation of Couples 9
            3.1.1 Gaussian copula 11
            3.1.2 Simulation of Gaussian copula 11
            3.1.3 The skewed t copula 12
            3.1.4 Simulation of the skewed t copula 14
            3.1.5 The Panic Couple 15
            3.1.6 The simulation of the Panic Couple 16
            3.4 Risk measurement 17
            3.4.1 Value at Risk (VaR) 17
            3.4.2 Conditional Value at Risk (CVaR) 18
            4. The empirical study of Mean-CVaR method on European Call options 22
            4.1 Data selection 22
            4.1 Scenario Simulation 24
            4.1.1 Scenario Simulation of group 1 25
            4.1.2 Scenario Simulation of group 2 27
            4.1.3 Scenario Simulation of group 3 30
            4.3 The VaR and CVaR of portfolios 32
            4.3.1 Optimization Algorithm 32
            4.3.2 The Optimization for CVaR 34
            5. Conclusion 37
            6. Reference 38
            7. Appendix 40
            7.1 The R code of Monte Carlo method with Gaussian Couple 40
            7.2 The R code of Monte Carlo method with Panic Couple 42
            7.3 The R code of Monte Carlo method with Skewed t  Couple 45
            7.4 The Ample code and results of optimization 48
             
            1. Introduction
            1.1 Motivation
            In the past twenty years, the international financial market has undergone tremendous changes.  Since the 1980s, the development of financial liberalization, information technology, financing securitization and financial innovation have promoted the process of financial globalization. The deepening of financial innovation has made financial markets more volatile and the financial institutions will face more risk.  Thus, how to manage and control risk of investment are being increasingly important. In addition, after economic crisis in 2008, lots of people start to pay more attention on management and measure of risk in order to reducing their risk.Risk management involves in obtaining an expected profit with an acceptable risk. There are many different risk types and some of them cannot be eliminated.Although there are risks that cannot be diversified, we still can minimize risk by making a portfolio of different underlying assets.However, how to optimize portfolios becomes a crucial problem.
             
            Value at Risk (VaR) is a method that can use the standard statistical techniques to completely measure the market risk, which meets the needs for risk management. Morgan (1995) has firstly proposed the method of VaR measuring the market risk. As the technique can simply and effectively express the risk faced by financial asset, the VaR has become a common method of measuring the financial risk, has been widely used in practice. However, according to Artzner et al. (1999), the VaR technology cannot display the interrelated structure between assets by describing the combined risk of multiple assets. In order to improve the method of VaR, Rockafellar&Uryasev (2000) proposed the Conditional Value at Risk (CVaR). The CVaR is also called Mean Excess Loss, Tail VaR and Mean Shortfall, which is the same concept as Expected Shortfall. CVaR is a new approach to optimizing portfolio and can be used in asymmetric risk factors and it’s the expected loss exceeding VaR (Uryasev et al., 2002). Agarwal &Naik (2004) claimed that the preformation of CVaR is better than the mean-variance when risk is nonlinear. 
             
            There are lots of researches on the CVaR theories having been done. Moreover, the most research on CVaR involve stocks. However, we put our eyes on options part. Options are contracts that allow holders to buy or sell an asset on a certain date in the future with per determined price. There are generally two types of option, the European Option and the American Option. The mainly difference between them is European Option must be exercised on the pre-determined day while American Option could be exercised any time before the pre-determined day. Pricing for European Option is a well-researched area and previous studies include Black-Scholes. Since European Option is easier to analyse, we focus on portfolio consisting of a series of European Call options on stocks in this paper.
             
            1.2 Research question
            This research will focus on the portfolio consisting of a series of European Call options on stocks in this paper. In addition, we will apply algorithms used in simulating loss and use Monte Carlo Simulations during applying copulas in order to generate scenarios.  After the Monte Carlo Simulations, this research will investigate the find optimal portfolio of European Call options using the Mean-CVaR method. 
            .............................
            Conclusion
            Risk management involves in obtaining an expected profit with an acceptable risk. Value at Risk (VaR) is a method that can use the standard statistical techniques to completely measure the market risk. Rockafellar&Uryasev (2000) improved the measurement of VaR, and proposed the Conditional Value at Risk (CVaR), which is an effective approach to optimize portfolios. In the dissertation, we aim at using Mean-CVaR method to find optimal portfolio of American stock market. This research will use three basic couples of Gaussian Couple, Panic Couple and Skewed t couple to make scenarios simulation by Monte Carlo method. After that, by using the formula of Greeks linearized loss distribution, we can get the loss for the scenarios simulation of each stocks, that is, 〖 L〗_(t+1)^Δ=-(C_s^BS Δ+C_S^BS S_t X_(t+1,1)+C_σ^BS X_(t+1,2)). For the group 1, there is no obvious tail dependence on the linearized loss distribution of Gaussian Couple. 
            For the linearized loss distribution of Panic Couple of group 1, there are some tail dependence lying the upper right. For the linearized loss distribution of skewed t couple of group 1, there are some tail dependence lying the lower left, and there are slight tail dependence lying upper right.  The scatter plot of linearized loss distribution of group2 and group 3 shows that there is no obvious tail dependence on the both Gaussian couple and Panic Couple. For the linearized loss distribution of skewed t couple of both group 2 and group 3, there are heavy tail dependence lying upper right. 
            Lastly, this research will examine the effect the different types of copulas have on the structure of optimal portfolios in CVaR.  According to McNeil et al. (2005), 
            CVaR=Φ(ω)=min┬(y∈R^m )?〖F_β (ω,α)〗. The objective of this research is translated to the minimum of F_β (ω,α). By using the auxiliary function, the optimization problem of CVaR can be simplified as the linear programming problem. Using the software of Ampl, the results of the optimization problem on CVaR shows that the highest value of CVAR lies in the Panic couple distribution of group 1 and the Skewed-t Couple distribution of group 3. In other words, the CVaR has the same direction with the stock price. Moreover, the couple selection is closely related to the optimal portfolio, and the weight of optimal portfolio is relatively related to the correlation level.
            Reference
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            JP Morgan, RiskMetrics Technical Manual, New York, JP Morgan Bank, 1995
            Hendricks, D. (1996). Evaluation of value-at-risk models using historical data.
            Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (1999). Coherent measures of risk. Mathematical finance, 9(3), 203-228.
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            Rockafellar, R.T. and Uryasev, S., 2002. Conditional value-at-risk for general loss distributions. Journal of banking & finance, 26(7), pp.1443-1471. ?
            McNeil, A.J., Frey, R., and Embrechts, P., 2005. Quantitative Risk Management: Concepts, Techniques, Tools, Princeton Series in Finance, Princeton University Press. 
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