Mathematical Modeling in Finance with Stochastic Processes

(Ben Green) #1

Chapter 2


Binomial Option Pricing


Models


2.1 Single Period Binomial Models


Rating


Student: contains scenes of mild algebra or calculus that may require guid-
ance.


Section Starter Question


Two items can be purchased in any amounts each, call the amountsxand
y. (Think about stocks and bonds.) The two items each contribute revenue
at rates specific to the current financial environment. (Think about stock
profits in good times and bad, call themrgxandrbxand bond interest at
ratesrgy andrby.) Two specific outcomes must be achieved, one in good
times, one in bad times (call themfgandfb). What mathematical set-up is
required to find the specific amounts of each item?


Key Concepts



  1. The simplest model for pricing an option is based on a market having
    a single period, a single security having two uncertain outcomes, and a
    single bond.


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