Python Backward Induction Overview

This project was written as a (very hurried) introduction to python for those who understand how to make induction trees in Excel. Look at the Notebook to see how it's run.

Python Basics

• Anything that is imported is usually imported by a name and then accessed via name.
  • E.g., import somePackage as sp sp.someFunction(3,2)
• Indentation is what determines grouping
  • This is true for loops, classes, functions, etc
• Python functions all start with keyword def functionName followed by a list of parameters being passed in - E.g.,

          def addTwoNumbers(alpha, beta):
          newValue = alpha + beta
          return newValue

Python Class Basics

• Python class definitions start with the keyword class and then lists the methods that are being defined. - If a class derives from anther class, that base class functions are available to the upper class. - Sometimes we overwrite these classes
• Class method functions always have a reference to the object. This is always ‘self’
  • E.g.,

       class SomeClass(object):
       def sayHello(self):
       print(“hello!”)

Tree Induction Object Basics

In order to create a new type of tree, you need to do the following:

• Define a new tree node class
• Create a new tree node factory
• Define a new tree info class (which derives from it.InfoObject)

Tree Node Class

The new tree node class has to derive from it.BaseTreeNode and needs two functions to be overwritten:

• def updateLocal(self, info):

  • Using the info passed in, updates any variables that depend on the nodes position in the tree. You can access - timestep - state (from 0 to timestep – 1) - stateInt – deviation from center ( 0 is center, 1 is one node up, -2 is two nodes down) = (-timeStep) + 2 * (state)

• def backInduct(self, info): 0 Using the tree info and nextUpper node and nextLower node (if not isFinalNode), calculate anything needed using backward induction

Tree Node Factory

To create a factory, one needs to

• Pass in new Tree node class
• Set any printing format of variables we want to print out

europeanPutFactory = it.TreeFactory(EuropeanPutNode)
europeanPutFactory.addForm('value', '%6.2f')
europeanPutFactory.addForm('price', '%6.2f')

Tree Info Class

To create a tree info class, you need to:

• Create a set of default values. This is a dictionary.
• Copy the def init function changing the names as appropriate
  • (This function is the constructor for this class. It’s ok if you don’t know what that means yet)
• Create a calc() function that calculates any derived values.

Using the Induction Tree

To use the tree,

• Start your favorite python interpreter. I recommend using Jupyter notebooks to run this notebook.
• Import your new file
• Create a new info object from your new file
• Create a tree using factory from file and new info object
• Print out variables of interest