How to Prepare for Financial Engineering Programs, Part 2

Joy Pathak

Swaptionz
This is Part 2 of my popular post, How to prepare for Financial Engineering programs. I finished all my refreshers in the Baruch MFE program at the end of August but I have been very busy with the classes to actually finish this article. This post will include topics, books, information I learnt/used in the refreshers and suggestions on how someone can cover these topics by themselves. I will break the topics according to the four refreshers I went through. For obvious reason I will not go into the excessive details of what was taught in the refreshers, but I will touch upon the general topics one should cover before starting a financial engineering program. In this post I give very specific topics and books one should go through before entering a MFE program. This post is not as general as the one before. Do remember that the Baruch College refreshers are notorious for being very rigorous. There is more material covered in four weeks than would be in a whole semester.

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).
  1. Parsing CSV files and manipulating the data to calculate various measures/ratios.
  2. Utilizing Boost libraries
  3. Using Classes effectively
  4. Using the Standard Template Library
  5. Understanding of functions, Inheritance, Polymorphism.
These are the topics that I believe are important for someone who will be entering a financial engineering program, especially Baruch. Going through the ENTIRE Savitch book will give anyone a strong base in C++ and then you can utilise the knowledge learnt in the numerical analysis sense in the program. The rest you will be taught in your respective programs hopefully. If you are not taught C++ in your MFE program, I would re-think joining that program if it was me as it is crucial to success in this industry. There are parts of Quantitative finance where other languages are used but it is a fact that C++ is widely used.

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:
  1. General Differentiation, Integration(definite & indefinite)
  2. Numerical Integration techniques like Simpson’s method.
  3. Taylor Series and approximations
  4. Finite Difference methods (forward, backward, central finite)
  5. Multivariable Calculus (chain rule, integration by parts, minimum/maximum)
  6. Lagrange Multipliers
Most of these topics have strong financial applications as can be seen in the Primer book. The book goes through all the applications from bond price calculations to Black Scholes call/put pricing, implied volatility, bootstrapping to find yield curves, etc. A complete review of this book by me can be found 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:
  1. Matrix Addition,Multiplication,etc
  2. Eigen values, Eigenvectors
  3. Applications to Complete Markets
  4. Algorithms to solve N dimensional linear equations (basics)
  5. Algorithms to find eigenvalues and eigenvectors.
  6. LU decomposition, Gaussian elimination
These are some of the topics that should be an absolute must before entering an MFE program in terms of algebra. The rest/advanced topics should or probably will be taught in the program.
Books I used to study Algebra:
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:
  1. Probability Measure (basics)
  2. Conditional Probabilities
  3. Independence
  4. Expectation, Variance
  5. Joint Distribution, Conditional Distributions, Marginal Distributions
  6. Everything in Discrete time and continuous time
  7. Law of large numbers and Central Limit theorem
These topics are almost always covered in any undergraduate course so one should already be familiar with all these concepts. It is up for debate if a strong understanding of the proofs and theoretical information associated with probability is required. We go through a rigorous proof based probability refresher at Baruch. This is primarily to aide us in the Probability and Stochastic Processes course in the fall semester which is quite proof based. The Stochastic Processes course is the pre-requisite for the Stochastic Calculus course that will be taught in Spring 2011.
Books I used to prepare for 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.
 
Thank you Joy!! Your posts about the preparation needed for an MFE are always very helpful!!
Looking forward to the next one ;)
 

cgorac

Active Member
Suggestions from Joy would probably have much more weight than mine, but I'd like to add my 2 cents regarding good book on some of above topics:

As for C++, back then when I was learning the language, the "C++ Primer" book by Stan Lippman served me very well. On the other side, for someone knowledgeable in C++, I'd certainly suggest reading Stroustrup's "The C++ Programming Language" for the refresher.

As for probability and statistics, I found DeGroot/Schervish "Probability and Statistics" (became aware of this book as it was used as textbook for MIT 18.05 course) very good - it's somewhat dry, and pretty much on the formal mathematical side, but the amount of information packed in is awesome.
 

davix

New Member
I was wondering which one is a better book for preparation:

1)A Primer for the Mathematics of Financial Engineering
2)Principles of financial engineering

I am considering buying one of them to prepare for my future MFE program but I am wondering which one should I purchase or maybe will it be even more beneficial if I buy both.
 

Joy Pathak

Swaptionz
Hello Davix,

I would suggest buying the Primer. The Principles of Financial Engineering book is an advanced book. You are better of buying Nefcti's Mathematics of Finance related book first and then Principles. I personally would suggest the Primer at this time, and once you have a strong understanding of that book you can jump onto more advanced books as the Principles of FE and Math Fin book by Nefcti.
 

rohitr

New Member
This is Part 2 of my popular post, How to prepare for Financial Engineering programs. I finished all my refreshers in the Baruch MFE program at the end of August but I have been very busy with the classes to actually finish this article. This post will include topics, books, information I learnt/used in the refreshers and suggestions on how someone can cover these topics by themselves. I will break the topics according to the four refreshers I went through. For obvious reason I will not go into the excessive details of what was taught in the refreshers, but I will touch upon the general topics one should cover before starting a financial engineering program. In this post I give very specific topics and books one should go through before entering a MFE program. This post is not as general as the one before. Do remember that the Baruch College refreshers are notorious for being very rigorous. There is more material covered in four weeks than would be in a whole semester.

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).
  1. Parsing CSV files and manipulating the data to calculate various measures/ratios.
  2. Utilizing Boost libraries
  3. Using Classes effectively
  4. Using the Standard Template Library
  5. Understanding of functions, Inheritance, Polymorphism.
These are the topics that I believe are important for someone who will be entering a financial engineering program, especially Baruch. Going through the ENTIRE Savitch book will give anyone a strong base in C++ and then you can utilise the knowledge learnt in the numerical analysis sense in the program. The rest you will be taught in your respective programs hopefully. If you are not taught C++ in your MFE program, I would re-think joining that program if it was me as it is crucial to success in this industry. There are parts of Quantitative finance where other languages are used but it is a fact that C++ is widely used.

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:
  1. General Differentiation, Integration(definite & indefinite)
  2. Numerical Integration techniques like Simpson’s method.
  3. Taylor Series and approximations
  4. Finite Difference methods (forward, backward, central finite)
  5. Multivariable Calculus (chain rule, integration by parts, minimum/maximum)
  6. Lagrange Multipliers
Most of these topics have strong financial applications as can be seen in the Primer book. The book goes through all the applications from bond price calculations to Black Scholes call/put pricing, implied volatility, bootstrapping to find yield curves, etc. A complete review of this book by me can be found 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:
  1. Matrix Addition,Multiplication,etc
  2. Eigen values, Eigenvectors
  3. Applications to Complete Markets
  4. Algorithms to solve N dimensional linear equations (basics)
  5. Algorithms to find eigenvalues and eigenvectors.
  6. LU decomposition, Gaussian elimination
These are some of the topics that should be an absolute must before entering an MFE program in terms of algebra. The rest/advanced topics should or probably will be taught in the program.
Books I used to study Algebra:
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:
  1. Probability Measure (basics)
  2. Conditional Probabilities
  3. Independence
  4. Expectation, Variance
  5. Joint Distribution, Conditional Distributions, Marginal Distributions
  6. Everything in Discrete time and continuous time
  7. Law of large numbers and Central Limit theorem
These topics are almost always covered in any undergraduate course so one should already be familiar with all these concepts. It is up for debate if a strong understanding of the proofs and theoretical information associated with probability is required. We go through a rigorous proof based probability refresher at Baruch. This is primarily to aide us in the Probability and Stochastic Processes course in the fall semester which is quite proof based. The Stochastic Processes course is the pre-requisite for the Stochastic Calculus course that will be taught in Spring 2011.
Books I used to prepare for 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.
Hi Joy!

Can you also mention the amount of time per day or how many months did it take you to complete these books individually,i.e no. of months per book.

Also,will I require to brush up my calculus before reading the primer by Dan Stefanica?

I read RS agarwal in school. I learnt basic integration and differentiation in school. I'm not sure whether I remember anything or not.
 

edgerr

New Member
This is Part 2 of my popular post, How to prepare for Financial Engineering programs. I finished all my refreshers in the Baruch MFE program at the end of August but I have been very busy with the classes to actually finish this article. This post will include topics, books, information I learnt/used in the refreshers and suggestions on how someone can cover these topics by themselves. I will break the topics according to the four refreshers I went through. For obvious reason I will not go into the excessive details of what was taught in the refreshers, but I will touch upon the general topics one should cover before starting a financial engineering program. In this post I give very specific topics and books one should go through before entering a MFE program. This post is not as general as the one before. Do remember that the Baruch College refreshers are notorious for being very rigorous. There is more material covered in four weeks than would be in a whole semester.

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).
  1. Parsing CSV files and manipulating the data to calculate various measures/ratios.
  2. Utilizing Boost libraries
  3. Using Classes effectively
  4. Using the Standard Template Library
  5. Understanding of functions, Inheritance, Polymorphism.
These are the topics that I believe are important for someone who will be entering a financial engineering program, especially Baruch. Going through the ENTIRE Savitch book will give anyone a strong base in C++ and then you can utilise the knowledge learnt in the numerical analysis sense in the program. The rest you will be taught in your respective programs hopefully. If you are not taught C++ in your MFE program, I would re-think joining that program if it was me as it is crucial to success in this industry. There are parts of Quantitative finance where other languages are used but it is a fact that C++ is widely used.

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:
  1. General Differentiation, Integration(definite & indefinite)
  2. Numerical Integration techniques like Simpson’s method.
  3. Taylor Series and approximations
  4. Finite Difference methods (forward, backward, central finite)
  5. Multivariable Calculus (chain rule, integration by parts, minimum/maximum)
  6. Lagrange Multipliers
Most of these topics have strong financial applications as can be seen in the Primer book. The book goes through all the applications from bond price calculations to Black Scholes call/put pricing, implied volatility, bootstrapping to find yield curves, etc. A complete review of this book by me can be found 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:
  1. Matrix Addition,Multiplication,etc
  2. Eigen values, Eigenvectors
  3. Applications to Complete Markets
  4. Algorithms to solve N dimensional linear equations (basics)
  5. Algorithms to find eigenvalues and eigenvectors.
  6. LU decomposition, Gaussian elimination
These are some of the topics that should be an absolute must before entering an MFE program in terms of algebra. The rest/advanced topics should or probably will be taught in the program.
Books I used to study Algebra:
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:
  1. Probability Measure (basics)
  2. Conditional Probabilities
  3. Independence
  4. Expectation, Variance
  5. Joint Distribution, Conditional Distributions, Marginal Distributions
  6. Everything in Discrete time and continuous time
  7. Law of large numbers and Central Limit theorem
These topics are almost always covered in any undergraduate course so one should already be familiar with all these concepts. It is up for debate if a strong understanding of the proofs and theoretical information associated with probability is required. We go through a rigorous proof based probability refresher at Baruch. This is primarily to aide us in the Probability and Stochastic Processes course in the fall semester which is quite proof based. The Stochastic Processes course is the pre-requisite for the Stochastic Calculus course that will be taught in Spring 2011.
Books I used to prepare for 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.
Hi Joy! Will I have to finish some other calculus book before reading the primer book by dan stefanica? Plz tell me as to how you brushed up your calculus before starting the primer.
Also,are the basics about the black scholes,monte carlo,taylor series etc easily explained in this book?
 

edgerr

New Member
This is Part 2 of my popular post, How to prepare for Financial Engineering programs. I finished all my refreshers in the Baruch MFE program at the end of August but I have been very busy with the classes to actually finish this article. This post will include topics, books, information I learnt/used in the refreshers and suggestions on how someone can cover these topics by themselves. I will break the topics according to the four refreshers I went through. For obvious reason I will not go into the excessive details of what was taught in the refreshers, but I will touch upon the general topics one should cover before starting a financial engineering program. In this post I give very specific topics and books one should go through before entering a MFE program. This post is not as general as the one before. Do remember that the Baruch College refreshers are notorious for being very rigorous. There is more material covered in four weeks than would be in a whole semester.

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).
  1. Parsing CSV files and manipulating the data to calculate various measures/ratios.
  2. Utilizing Boost libraries
  3. Using Classes effectively
  4. Using the Standard Template Library
  5. Understanding of functions, Inheritance, Polymorphism.
These are the topics that I believe are important for someone who will be entering a financial engineering program, especially Baruch. Going through the ENTIRE Savitch book will give anyone a strong base in C++ and then you can utilise the knowledge learnt in the numerical analysis sense in the program. The rest you will be taught in your respective programs hopefully. If you are not taught C++ in your MFE program, I would re-think joining that program if it was me as it is crucial to success in this industry. There are parts of Quantitative finance where other languages are used but it is a fact that C++ is widely used.

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:
  1. General Differentiation, Integration(definite & indefinite)
  2. Numerical Integration techniques like Simpson’s method.
  3. Taylor Series and approximations
  4. Finite Difference methods (forward, backward, central finite)
  5. Multivariable Calculus (chain rule, integration by parts, minimum/maximum)
  6. Lagrange Multipliers
Most of these topics have strong financial applications as can be seen in the Primer book. The book goes through all the applications from bond price calculations to Black Scholes call/put pricing, implied volatility, bootstrapping to find yield curves, etc. A complete review of this book by me can be found 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:
  1. Matrix Addition,Multiplication,etc
  2. Eigen values, Eigenvectors
  3. Applications to Complete Markets
  4. Algorithms to solve N dimensional linear equations (basics)
  5. Algorithms to find eigenvalues and eigenvectors.
  6. LU decomposition, Gaussian elimination
These are some of the topics that should be an absolute must before entering an MFE program in terms of algebra. The rest/advanced topics should or probably will be taught in the program.
Books I used to study Algebra:
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:
  1. Probability Measure (basics)
  2. Conditional Probabilities
  3. Independence
  4. Expectation, Variance
  5. Joint Distribution, Conditional Distributions, Marginal Distributions
  6. Everything in Discrete time and continuous time
  7. Law of large numbers and Central Limit theorem
These topics are almost always covered in any undergraduate course so one should already be familiar with all these concepts. It is up for debate if a strong understanding of the proofs and theoretical information associated with probability is required. We go through a rigorous proof based probability refresher at Baruch. This is primarily to aide us in the Probability and Stochastic Processes course in the fall semester which is quite proof based. The Stochastic Processes course is the pre-requisite for the Stochastic Calculus course that will be taught in Spring 2011.
Books I used to prepare for 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.
Hi,
Tell me the strategy that you used to finish the book 'problem solving with c++'.
Did you also solve EOC practice ques and programming projects?
 
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