Risk Management (Probability modeling in finance and economics) Essay

Risk Management (Probability modeling in finance and economics) - Essay Example ARCH and GARCH type models used to estimate volatility are also nonlinear models expressed as a function (linear or not) of past variations in stocks. ARCH-GARCH models and more recently the range process have generated an extensive amount of research and papers. Just as chaos the Hurst, exponent and memory modeling have been topics of interest in many areas outside finance and economics. ARCH and GARCH models, which are important for modeling and estimating volatility, are an important part of modern finance. Since the value of an option depends essentially on its volatility and volatility studies are assuming an important role in financial modeling. A primary feature of the autoregressive Conditional heteroscedasticity (ARCH) model as developed by Engle (1982), is that the conditional variances change over time. Following the seminal idea, numerous models incorporating this feature have been proposed. Among these models, Bollerslev's (1986) generalized ARCH (GARCH) model is certainly the most popular and successful because it is easy to estimate and interpret by analogy with the autoregressive moving average (ARMA) time series model. ... prominent role in the analysis of many aspects of financial econometrics such as the term structure of interest rates, the pricing of options, the presence of time varying risk premia in the foreign exchange market. The quintessence of the ARCH model is to make volatility depend on variability of past observations. An alternative formulation initiated by Taylor (1986) makes volatility be driven by unobserved component, and has come to be known as the stochastic volatility (SV) model. AS for the ARCH models SV models have also been intensively used in the last decade, especially after the progress accomplished in the corresponding estimation techniques, as illustrated in the excellent surveys of Ghysels ET al (1996) and Shepard (1996). Early contributions that aimed at relating changes in volatility of asset returns to economic intuition include Clark (1973) who assumed that a stochastic process of information arrival generates a random number of intraday changes of the asset price. The Black-Scholes model for instance assumes that the price of the asset underlying the option contract follows a geometric Brownian motion and one of the most successful extensions has been the continuous time SV model. In these models, volatility is not a constant as in the original Black-Scholes model; rather, it is another random process typically driven by a Brownian motion that is imperfectly correlated with the Brownian motion driving the primitive asset price dynamics. In technical terms, the volatility process generated within arch type models converges in distribution towards a well-defined solution of a stochastic differential equation as the sampling frequency increases. One concomitant reason is that the continuous record asymptotics developed for the ARCH models do not deliver

Mercy killing Essay Example | Topics and Well Written Essays - 2000 words

Mercy killing - Essay Example The terminology mercy killing on the other hand refers to someone taking a direct action to terminate the life of a patient without permission from the patient. The decision to take such an action is usually made on the assumption that the patient’s life is no longer meaningful or that if the patient was in a position to say so, he would express his desire to die (Padilla 219). The distinction between mercy death and mercy killing is that mercy death is voluntary and is conducted with the permission of the patient and often at his request while mercy killing is involuntary and does not involve the patient’s permission or request. None of the actions is more morally acceptable than the other and arguments exist against these actions. Many arguments used against suicide are applicable to mercy death to some extent but the issues surrounding mercy death are complicated by the fact that another person has to do the killing (Padilla 227). If patients who request for mercy de ath would wait to see the results of medical therapy and science, they would probably adjust to their situations and change their minds about dying. Mercy killing is also complicated by the fact that it is done without the consent of the patient and this is a violation of the Value of Life Principle, no one has the right to decide whether a person’s life is worthy. Human beings also have rights and they are not the same as those of animals and no matter what science may say no human being is merely an animal. Question 2: What are the arguments for and against mercy death? Is it morally justifiable in some situations? The first argument about mercy death is that people who are suffering and in pain are usually in a state of fear and depression and therefore cannot simply make rational decisions, if such patients were to wait and see what medical science and therapy can do for them they would probably adjust to their situation and change their minds about dying. The second argu ment states that just as we are generally willing to put animals out of their misery when they suffer, we should do the same for human beings but the rights of human beings to live and die are not the same as those of animals. Western religions maintain that human beings have immortal souls and even non religious humanists talk about the human spirit or personality stating that it should be accorded greater respect than the mere physical self (Padilla 230). Mercy killing is a direct violation of the Principle Value of Life mainly because it involves taking the life of an innocent person, murder is murder regardless of the motive and this is cemented by the fact that patients have not or cannot give their consent for the termination of their lives. The domino argument states that because the consent of patients cannot be obtained, an outside decision about the worth, value and meaning of a patient’s life has to be made but this is a dangerous move because no one has the right to decide if a person’s life is worthy, has value or is meaningful. There is also a possibility of finding cures in future and patients could therefore continue living. In cases of financial and emotional burdens to the family but finances and emotions should not be determining factors where human life is concerned. Both mercy death and mercy killing are not morally justifiable because humane alternatives for both mercy death an