Dynamic Financial Risk Management

Abstract

For many years, financial markets have been part of people’s everyday life. Information on the major securitiescan be found easily in the daily press or on internet. The different actors of the economy look closely at somefundamental parameters, such as interest rates, currency rates, stock prices..., which may affect the managementof their firms, especially after the deregulation process initiated in the United States in the 1970s. The accruedinternational dimension and efficiency of the communication means have extended this phenomenon to the entireworld economy. Small investors savings and pensions are also exposed to the risks generated by variations inthese factors.Financial institutions are aware of the importance of managing these risks. They offer different solutions, whichwill be presented below. For instance, the following product can help small investor to deal with variations ofthe stock markets:In 2005, bank XYZ offered the following product, which is a 5 years guaranteed capital fund:• 0% of the yield of a basket of six indices when it is negative.• 50% of the yield if lower than 50%• 25%+ 100% of the yield if greater than 50%The basket is build with six financial indices from different international markets: FTSE 89, SMI, FTSE100,NIKKEI225, S&P500, Hang Seng.More generally, in order to deal with variations in fundamental financial and economic factors, a large varietyof financial instruments has been created. Simple derivative contracts (futures, options, swaps, etc.) or moreexotic financial products (credit derivatives, catastrophe bonds, exotic options, etc.) are offered to privateand institutional investors to transfer their financial risks to specialized financial institutions in exchange of asuitable compensation. The organized markets, on which these products are traded, are fully devoted to themanagement of (fundamental) financial risks. They can be seen as financial risk markets. As argued by Merton[36], the development of the financial risk industry would not have been possible without the developmentand support of theoretical tools. Mathematics has emerged as the leading discipline to address fundamentalquestions related to financial risk management. Mathematical finance, which applies the theory of probabilityand stochastic processes to finance, in particular Brownian motion and martingale theory, stochastic controland partial differential equations, is now a field of research in its own.