Chapter 1 Financial Markets and Derivatives 1.1. Financial Markets A (primary) financial market consists of tradable securities such as stocks, bonds, currencies, commodities, or even indexes. One reason for the ex- istence of financial markets is that they facilitate the flow of capital. For example, if a company wants to finance the building of a new production facility, it might sell shares of stock to investors, who buy the shares based on the anticipation of future rewards such as dividends or a rise in the stock price. A variety of stochastic models is used in modeling the prices of securities. All such models face the usual trade off: more complex models typically provide a better fit to data (although there is the danger of overfitting), whereas simpler models are generally more tractable and despite their sim- plicity can sometimes provide useful qualitative insights. Finding a good balance between a realistic and a tractable model is part of the art of sto- chastic modeling. Both discrete (in time and state), and continuous (in time and state) models will be considered here. The treatment of discrete time models is intended as a means of introducing notions such as hedging and pricing by arbitrage in a simple setting and to provide a bridge to the development in the continuous case. Binomial tree models are the most common example in the discrete case. Our treatment of discrete and continuous models is not meant to be exhaustive, but rather to provide an introduction that will enable students to go on to read more advanced material. 1 http://dx.doi.org/10.1090/gsm/072/01
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