#### Joy Pathak

##### Swaptionz

**1. PROGRAMMING**

Since programming was my first refresher and the building block for most of the other courses I figured I would talk about it first. I would definitely recommend to everyone who is entering the world of financial engineering to build up on their C++. C++ is the most widely used programming language in Quantitative finance. To prepare for C++ as I mentioned before I went through a list of the books I outlined in my previous post. In the C++ refresher as I mentioned in another post (

**Exponential Learning Part 1**), I used the Walter Savitch book Problem Solving with C++. Some of the topics that one has to be very familiar with before entering a financial engineering program are the following (no order).

- Parsing CSV files and manipulating the data to calculate various measures/ratios.
- Utilizing Boost libraries
- Using Classes effectively
- Using the Standard Template Library
- Understanding of functions, Inheritance, Polymorphism.

I basically went through the Savitch book and solved a range of problems from behind the book. We were given in our refresher course two major projects to do at the end of the course where-in we utilised a range of tools we learnt to full-fill the requirements of the project.

__Book I used for C++:__

**2. MATHEMATICS FOR FINANCIAL ENGINEERING**

I am going to break this part into two. The first part with deal with the mathematics one should have a good grasp on before entering the program which is directly used in quantitative finance. The first part will focus more on the advanced calculus topics whereas the second will focus on the Algebra topics.

**a)**

__Mathematical Finance/Advanced Calculus__Mathematical finance for this post means primarily advanced calculus concepts with application to finance. In our class we utilised, A Primer For The Mathematics Of Financial Engineering as our main book for the course. This book is definitely a MUST HAVE for every financial engineering student. Some of the concepts that a student must ABSOLUTELY know before entering an MFE program should be:

- General Differentiation, Integration(definite & indefinite)
- Numerical Integration techniques like Simpson’s method.
- Taylor Series and approximations
- Finite Difference methods (forward, backward, central finite)
- Multivariable Calculus (chain rule, integration by parts, minimum/maximum)
- Lagrange Multipliers

**here**

__Book I used for Mathematical Finance:__

**a)**

__Advanced Algebra__Algebra is a vast field. The applications from Algebra to Finance are very specific. A good MFE program will go through all of these in extreme detail. There is a significant amount of Numerical Linear Algebra that is used in quantitative finance and should be taught in every program. Since at Baruch we have a whole course devoted to Numerical Linear Algebra I decided to just make sure I know the basic concepts very well and made sure I understood some of the common algorithms used in detail. Some of the topics that one should definitely know before entering an MFE program should be as follows:

- Matrix Addition,Multiplication,etc
- Eigen values, Eigenvectors
- Applications to Complete Markets
- Algorithms to solve N dimensional linear equations (basics)
- Algorithms to find eigenvalues and eigenvectors.
- LU decomposition, Gaussian elimination

__Books I used to study Algebra:__

- Introduction to Linear Algebra
- Lecture Notes provided by Dr. Dan Stefanica

**3. PROBABILITY/STATISTICS**

**a)**

__Statistics__This part is up for debate. Having a strong background in statistics is definitely important considering the amount of time series analysis that is conducted in quantitative finance. Having a good background in statistics definitely aided me in the Statistical Arbitrage class. It also helped me secure my job as Quantitative Strategist building and testing statistical arbitrage strategies for AQC. The benefits of having a strong statistics background can aide considerably depending on which field of finance one wants to enter. A strong econometrics course or advanced statistics course should help here. I conducted a lot of self study in econometrics and published a paper in the field too utilising significant amounts of factor modelling before entering the program.

__Books I used to prepare for Statistics:__

- Mathematical Statistics with Applications (used it in my class in Spring 2010 @ University of Windsor)
- Stat-Arb Primer made by myself and Dr. Jim Liew for Statistical Arbitrage class (This has not been published yet. It is in the works but will be used in future classes)

**b)**

__Probability__This mostly refers to probability theory, a precursor to Stochastic Processes and Stochastic Calculus. I utilised two books to study for this part. Both were also recommended in our refresher seminars. I learnt majority of the concepts in a more applied sense before coming to the refreshers, whereas majority of the items taught in the course were quite theoretical. Some of the topics that one should be very familiar with before entering the program should be:

- Probability Measure (basics)
- Conditional Probabilities
- Independence
- Expectation, Variance
- Joint Distribution, Conditional Distributions, Marginal Distributions
- Everything in Discrete time and continuous time
- Law of large numbers and Central Limit theorem

__Books I used to prepare for Probability:__

- Lecture Notes by Dr. Elena Kosygina
- A Natural Introduction to Probability Theory
- First Course in Probability

**4. FINANCE**

The reason I put finance at the end is because, most of finance can be picked up relatively easily in comparison to the mathematics part. Get a strong understanding of the programming and mathematics part and the basic finance knowledge can be easily gained from CFA level 1 , any introductory undergraduate finance course or book.

If you want to get a deeper understanding of finance in relation to particularly financial engineering, then the Hull book is a necessity. I personally used the new Hull book for all my finance preparation. The Primer for the Mathematics of Financial engineering by Dan Stefanica is also a good aide when it comes to the finance part considering there are many introductions to finance given, in the mathematical setting.

__Books I used to prepare for Finance:__

All in all, I believe I am very confident with what I know in terms of being ready for the program. I will make another post that will be part 2 of the Exponential Learning which will involve what I learnt in the last two refreshers and their review.

My first class was on Thursday for Probability and Stochastic Processes for Finance. I have Numerical Methods in Finance next, and then Object Oriented Programming in Finance after that. I will also be taking the Pricing of Financial Instruments course with Bob Spruill this fall semester. I wish there was some way of me overloading and taking Commodities Trading with Luis Molina (MD @ Credit Suisse Commodities Division) or Volatility Surface with Dr. Jim Gatheral, but I suppose that will have to wait for now.

Hope this helps! Feel free to post questions in the comments section. I will try my best to answer them all.