Mathematical Modeling in Finance with Stochastic Processes

64 CHAPTER 1. BACKGROUND IDEAS

2. Weisstein, Eric W. “Stochastic Process.” From MathWorld–A Wolfram
   Web Resource. Stochastic Process


3. Weisstein, Eric W. “Markov Chain.” From MathWorld–A Wolfram
   Web Resource. Markov Chain


4. Weisstein, Eric W. “Markov Process.” From MathWorld–A Wolfram
   Web Resource. Markov Process


5. Julia Ruscher studying stochastic processes

1.8 A Binomial Model of Mortgage Collater-

alized Debt Obligations (CDOs)

Rating

Mathematically Mature: may contain mathematics beyond calculus with
proofs.

Section Starter Question

How do you evaluate cumulative binomial probabilities when the value ofn
is large, and the value ofpis small?

Key Concepts

1. We can make a simple mathematical model of a financial derivative
   using only the idea of a binomial probability.


2. We must investigate the sensitivity of the model to the parameter values
   in order to completely understand the model.


3. This simple model provides our first illustration of the model cycle
   applied to a situation in mathematical finance, but even so, it yields
   valuable insights.