RESEARCHES ON NEW MEASUREMENT METHODS FOR MARKET RISK, CREDIT RISK AND LIQUIDITY RISK IN FINANCIAL MARKETS.

1987年美国黑色星期一、日本股市崩盘、金融机构不良贷款问题、90年代企业违约事件增多等重大金融事件，都强烈地引起了我们的注意，需要新的方法来衡量各种金融风险，如市场风险、信用风险、流动性风险等。本研究是一个现实而具体的答案，我们提出了新的方法来评估和衡量除流动性风险。本文首先介绍了双曲正弦（HS）随机过程，这是金融研究中一个非常新颖的概念。检验真实市场中收益的正态假设（分布和/或过程），接受该假设似乎值得怀疑，特别是它不能解释收益分布中的肥尾结构。如果我们否定正常假设，将会对依赖于正常假设的传统金融研究产生很大的影响。在我们的研究中，在对返回的数据进行HS变换后，我们很快意识到这个过程使分布近似正态分布。利用这个简单的性质，我们证明了它可以度量市场和信用的风险价值（VaR），并且也适用于肥尾问题和极值理论。接下来，我们考虑了PDE、Fynman-Kac定理、风险中性方法等多种方法，并将HS概念直接应用于欧美衍生品的定价，这些衍生品在股票/债券市场的基础证券收益依赖于HS过程。最后将其应用到结构性信用模型中，推导出新的信用风险评估和度量模型。

The big financial topics like the US Black Monday in 1987, and the Japanese stock market crash, the bad-loan problem involving financial institutions, and increasing of big corporate default events in 1990's have strongly come under our notice for new methods to measure the various kind of financial risks such as Market Risk, Credit Risk, Liquidity Risk, and so on. This research is one of the realistic and concrete answers, and we propose the new methods to evaluate and measure those risks except liquidity risk.We first introduce a Hyperbolic Sine (HS) stochastic process, a very new and original concept in financial study. Checking the Normal Hypothesis (distribution and/or process) of returns in the real markets, it seems doubtful to accept the Hypothesis, particularly it cannot explain the fat-tail structure in return distribution. If we deny the normal Hypothesis, it affects a lot to the traditional financial studies that strongly depend on the Hypothesis. In our researches, after taking a HS Transform to return data, we are soon aware that this process makes the distribution approximately normal. Using this simple property, we show the fact that it can measure the market and credit Value at Risk (VaR) and it is also applicable to the fat-tail problem and the extreme value theory.Next we take into account various methods like PDE, the Fynman-Kac theorem, and risk neutral method, and we directly apply our HS concept to price European and American derivatives whose underlying security returns in stock/bond market depend on HS process.Lastly we apply it to the structural credit model and derive our new models to value and measure the credit risks.