Financial Theory with Python

Chapter 6. Dynamic Economy

Multiperiod models of securities markets are much more realistic than single period models. In fact, they are extensively used for practical purposes in the financial industry.

Stanley Pliska (1997)

Although markets are not complete at any one time, they are dynamically complete in the sense that any consumption process can be financed by trading the given set of financial securities, adjusting portfolios through time as uncertainty is resolved bit by bit.

Darrell Duffie (1986)

In reality, quantitative information—such as changes in stock prices or interest rates—is revealed gradually over time. While static model economies are an elegant way of introducing fundamental notions in finance, a realistic financial model requires a dynamic representation of the financial world.

The formalism needed to properly model dynamic economies is more involved and cannot be covered in full detail in this chapter. However, the chapter can present two of the most important dynamic model economies based on discrete time dynamics: the Cox-Ross-Rubinstein (1979) binomial option pricing model and the Black-Scholes-Merton (1973) option pricing model in a discrete Monte Carlo simulation version. In this context, discrete time means that the set of relevant dates is extended from just two to a larger, but still finite, number—say, to five or 50.

The tools used in this chapter are more or less the same as before: linear algebra, probability theory, and also, like in the ...