Stochastic Processes for the Risk Management

Stochastic Processes for the Risk Management

Gamze Özel
DOI: 10.4018/978-1-5225-5481-3.ch023
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The financial markets use stochastic models to represent the seemingly random behavior of assets such as stocks, commodities, relative currency prices such as the price of one currency compared to that of another, such as the price of US Dollar compared to that of the Euro, and interest rates. These models are then used by quantitative analysts to value options on stock prices, bond prices, and on interest rates. This chapter gives an overview of the stochastic models and methods used in financial risk management. Given the random nature of future events on financial markets, the field of stochastic processes obviously plays an important role in quantitative risk management. Random walk, Brownian motion and geometric Brownian motion processes in risk management are explained. Simulations of these processes are provided with some software codes.
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Definitions of risk vary based on context. The International Organization for Standardization (ISO) in the ISO Guide 73 defines risk as the “effect of uncertainty on objectives” (ISO, 2009). The reason for a risk is uncertainty. Uncertainty is “the state of being uncertain.” Uncertain means “not able to be relied on; not known or definite.” Imagine that you would like to purchase a property in San Francisco, which is known for its susceptibility to earthquakes. We know that there is a risk of an earthquake occurring at any time, but we cannot say if there will be an earthquake during the next three years or not. It is uncertain.

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