Chapter 2Market Risk with the Normal Distribution

Regarding modern risk management, it is fair to say research and practice in market risk have played a very important role. The major financial economics breakthroughs were due to a rich body of contributions by academic researchers and practitioners. In 1990, Harry Markowitz, Merton Miller, and William Sharpe were jointly awarded the Nobel Prize in Economic Sciences for “their pioneer work in the theory of financial economics” in the 1950s and 1960s. They laid down a foundation of risk-based asset pricing and portfolio decision theory. Fisher Black, Myron Scholes, and Robert Merton's work on options successfully applied risk-based concepts such as replicating portfolio for hedging and law of no-arbitrage in asset pricing. Their work laureated Scholes and Merton (with an honorable mention of the late Black) the Nobel Prize in Economic Sciences in 1997.

Since the early risk researches and practice the multivariate normal distribution assumption for the changes in all the market risk and macroeconomic factors such as equity, foreign exchange, and interest rates is one of the most popular quantitative approaches. We will therefore start with market risk management using a multivariate normal distribution assumption. We will consider three different cases for the portfolio representation: first, the case of linear portfolios such as plain stock portfolios or portfolios that can be approximated well by a first-order sensitivity; second, ...

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