3. Nonlinearity in Finance | Mastering Python for Finance

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Table Of Contents

Mastering Python for Finance

3.3 (7)

Mastering Python for Finance

3.3 (7)

Overview of this book

If you are an undergraduate or graduate student, a beginner to algorithmic development and research, or a software developer in the financial industry who is interested in using Python for quantitative methods in finance, this is the book for you. It would be helpful to have a bit of familiarity with basic Python usage, but no prior experience is required.

Preface

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Free Chapter

1. Python for Financial Applications

1. Python for Financial Applications

Is Python for me?

Objected-oriented versus functional programming

Which Python version should I use?

Introducing IPython

Summary

2. The Importance of Linearity in Finance

2. The Importance of Linearity in Finance

The capital asset pricing model and the security market line

The Arbitrage Pricing Theory model

Multivariate linear regression of factor models

Linear optimization

Solving linear equations using matrices

The LU decomposition

The Cholesky decomposition

The QR decomposition

Summary

3. Nonlinearity in Finance

3. Nonlinearity in Finance

Nonlinearity modeling

Examples of nonlinear models

An introduction to root-finding

Incremental search

The bisection method

Newton's method

The secant method

Combining root-finding methods

SciPy implementations

Summary

4. Numerical Procedures

4. Numerical Procedures

Introduction to options

Binomial trees in options pricing

The Greeks for free

Trinomial trees in options pricing

Lattices in options pricing

Finite differences in options pricing

Putting it all together – implied volatility modeling

Summary

5. Interest Rates and Derivatives

5. Interest Rates and Derivatives

Fixed-income securities

Yield curves

Valuing a zero-coupon bond

Bootstrapping a yield curve

Forward rates

Calculating the yield to maturity

Calculating the price of a bond

Bond duration

Bond convexity

Short-rate modeling

Bond options

Pricing a callable bond option

Summary

6. Interactive Financial Analytics with Python and VSTOXX

6. Interactive Financial Analytics with Python and VSTOXX

Volatility derivatives

Gathering the EUROX STOXX 50 Index and VSTOXX data

Merging the data

Financial analytics of SX5E and V2TX

Correlation between SX5E and V2TX

Calculating the VSTOXX sub-indices

Calculating the VSTOXX main index

Summary

7. Big Data with Python

7. Big Data with Python

Introducing big data

Hadoop for big data

Is big data for me?

Getting Apache Hadoop

A word count program in Hadoop

Going deeper – Hadoop for finance

Introducing NoSQL

Summary

8. Algorithmic Trading

8. Algorithmic Trading

Introduction to algorithmic trading

List of trading platforms with public API

Which is the best programming language to use?

System functionalities

Algorithmic trading with Interactive Brokers and IbPy

Building a mean-reverting algorithmic trading system

Forex trading with OANDA API

Building a trend-following forex trading platform

VaR for risk management

Summary

9. Backtesting

9. Backtesting

An introduction to backtesting

Designing and implementing a backtesting system

Ten considerations for a backtesting model

Discussion of algorithms in backtesting

Summary

10. Excel with Python

10. Excel with Python

Overview of COM

Excel for finance

Building a COM server

Building the COM client in Excel

What else can I do with COM?

Summary

Index

Index

Incremental search

A crude method of solving a nonlinear function is by doing an incremental search. Using an arbitrarily starting point , we can obtain values of for every increment of . We assume that the values of , , … are going in the same direction as indicated by their sign. Once the sign changes, a solution is deemed as found. Otherwise, the iterative search terminates when it crosses the boundary point .

A pictorial example of the root-finder method for iteration is given in the following graph:

An example can be seen from the Python code:

'''
Python code:
Incremental search method
'''
""" An incremental search algorithm """
import numpy as np
 
 
def incremental_search(f, a, b, dx):
    """
    :param f: The function to solve
    :param a: The left boundary x-axis value
    :param b: The right boundary x-axis value
    :param dx: The incremental value in searching
    :return: The x-axis value of the root,
                number of iterations used
    """
    fa = f(a)    
    c...

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