Bridging Academics from the Classroom to Practice

New Class for NC State’s Financial Mathematics Graduate Program: Practical Portfolio Management.

The Masters of Financial Mathematics at NC State is offering a new course, Practical Portfolio Management.  This course is about bridging the gap between academic knowledge/modeling and the practice of managing a portfolio. If you are a student studying in a quant/finance field, you might have asked yourself questions like "how can I apply this theorem in practice?" or "how practitioner operate things in practice?" These questions are critical to successfully moving your academic knowledge from the classroom to the workplace.

The course starts by considering what contributes to the risk premium; business risk, financial risk, liquidity risk, exchange rate risk, and/or political risk. Students make their own asset allocation decisions, by first creating their own policy statement, creating an initial portfolio, then rebalancing their portfolio on a weekly basis.

currency rates

Portfolios can be composed of a wide variety of assets, such as the S&P 500 Index, Equity ETFs, Treasury bonds, Stocks, and etc., is a typical example. The course will cover the pros and cons of quantitative tools.  Decisions to adjust portfolios or asset allocations may be based on the managers’ view, or on more quantitative algorithmic strategies implemented in R (portfolio-trading) or Python (see crowdsourcing ideas leader Quantopian).

portfolio dashboard

A critical aspect of managing their portfolio is the justifications for the asset allocation and rebalancing decisions.  The decisions will be influenced by the rapidly evolving financial landscape, and will necessitate considerations of events that can have strong impacts on your portfolio, such as Brexit (see discussions by Schwab and Forbes), Greece returning to debt markets, and the November elections in the US.

profit target

The course will have a nontraditional structure.  The traditional lecture-homework-exam structure is replaced by actively managing their $100,000,000 portfolio throughout the semester. Similar courses are sometimes offered through extension courses, such as Options, Trading and Strategies at UCB and Strategic Portfolio Decisions at Stanford.

Richard Ellson

Dr. Richard Ellson created this course.  He recently joined NC State’s Masters of Financial Mathematics as an Adjunct Associate Professor. Dr. Ellson’s career started as a tenured professor at the University of South Carolina.  He was recruited to work at Wall Street firms and spent 25+ years in the finance industry. Richard has worked in several areas, and has deep experiences in residential whole loan mortgages and agency/non-agency mortgage-backed securities. His broad experience in research, trading/hedging, structured finance (domestic and foreign), and product development will guide FM students to success in their prospective career.

Textbook:  Analysis of Investments and Management of Portfolios. Keith C. Brown, Frank K. Reilly, 10th edition.

More about Dr. Ellson: http://www.ellsonconsulting.com

blog post created by J. Scroggs and Daihon Kwon.

 

Meet our Financial Math Alumni- Coffee chat with Albert Hopping- Part 2

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Part II: Analytic techniques continued...

6) Do you believe the future movement of the market data is, to some extent, driven by the models used by major financial institutions, even though these models may not be correct?

Albert: Does the market move because the model is assumed to be correct? I would say yes. Consider the market crash in 1987. Prior to the crash, there was no “volatility smile,” but there was after the crash. The market had actually been acting correctly, according to the model, until they realized the model made terrible assumptions. The market moved much more than their model implied. One event is meaningless; however, this highlights an incorrect model driving the market.

For a more current example, look to the way mortgages were priced before the recent mortgage bubble. Banks priced mortgages with the assumption that housing prices wouldn’t fall. The entire market priced that way because that was what everybody else did; it was group think. They used this assumption because the price had never gone down in their historical data set. Models are only as good as their assumptions. Could somebody have built a better model and actually predicted the housing price collapse? Yes, it could have been done and a few people did it.

Unfortunately, in a time of high earnings, it is easy to ignore risk. Risk is especially underweighted when quarterly earnings are prioritized over long term security. I feel that compensation packages are lagging the culture shift at most companies. This disconnect leads people to act as individuals focused on their personal bonuses rather than acting as representatives of their company. Further, a system which provides bailouts for bad behavior begets that bad behavior. The “smart” companies wouldn’t receive a bailout, leading some to assume they are better off to employ the incorrect group think model. Of course, this would not work in a free market.

7) Does your company use stochastic models? If it does, what kind of models are used?

Albert: We primarily work with customers who have reasons for the models they use. Sometimes, they ask us to implement specific models in their system. Other times, they come to us for advice asking what model may be best. For instance, in regards to interest rates, I am a big fan of the Libor Market Model (also known as the BGM Model). It is a term structure model. However, the industry almost exclusively seems to use short rate models. The Hull-White Model is very common because it’s very easy to parameterize, simple, and everyone else is using it.

However, I enjoy commodities more than interest rates or equities. In commodities, we have different issues because it is such a physical market. These models can be much more complicated. If I picked a favorite model, it is one that I was lucky enough to have helped develop (I’m biased). That model takes the term structure for a commodity and relates it back to the spot price allowing them to be simulated together. I really enjoy working with that model. In general, my favorite model is the right model for the situation; a model that makes logical sense and fits the data.

Part III: Risk management

8) How do the recent financial crisis and the regulation policies enacted after that affect the behavior of your company?

Albert: As a vendor, our business is based on our customers’ business. A crisis like that causes additional regulation or at least the changing of regulation. To handling that regulation it is very logical that a third party, a vendor would make a solution and sell it to customers. Typically, that type of regulation would cause a company like SAS to make a new product and be able to provide that solution to more people. Unfortunately, the capital expended on satisfying regulations cannot be used elsewhere in the economy.

9) The goal of risk management is to achieve a balance between returns and risks. Thus, with lots of capital and human resource spent, risk management may, to some extent, reduce a company’s profits. Now suppose you are a leader of a financial institution. Driven by the motivation of maximizing the profits, will you pay enough attention for risk management?

Albert: As a risk professional my answer must be yes. There are two aspects to consider in regards to risk: monitoring and management. Consider risk monitoring first. One should spend resource and pay attention to know the rules of the game. For an example, let’s think back to mortgages. What if housing prices could go down? I may go bankrupt. Well, that would be very important to know. If you don’t know the rules of the game, you cannot play your best.

In the same way, you need risk monitoring to help you see what the possibilities are. In terms of risk management, it’s like getting an insurance policy. Let’s say I have a house and all my money is in my house. If my house burns down, I may go bankrupt. I should clearly buy fire insurance on my house. That’s how risk management can be considered as well. Yes, if I am concerned about anything other than the very short term, I would spend enough resource on risk management and pay attention to my risk team.

Part IV: Suggestions & Advice

10) What skill sets are important to succeed in your field?

Albert: I get asked that question often: by students, by some of my friends, and some of my peers. I change the details of my answer almost every time, but there are key components that remain consistent. First and foremost is communication. No matter how smart you are, no matter how brilliant your model may be, if you cannot convince others and if you cannot explain your ideas, it is not going to matter.

Another component in my list is passion. Passion is not a skill, but an ingredient to success. Is it necessary? No. But if you are not passionate about your field, why work in it? Your passion allows you to have better ideas and think outside of the box which is critical. If you just think like everyone else, you are very replaceable. This makes it more difficult to advance. Your passion may present itself in the form of problem solving. This is an important skill.

Another skill of importance is programming. In our field, people are often not formally trained in programming. We are more likely to be self-taught with at most one or two university courses in programming. This is very different than those people who come out of school with an entire degree in computer science. They have different level of understanding the way a machine thinks. In some parts of our field, this understanding is critical and you will need to learn it. Being skillful enough to have a computer automate you work is always important. Automation frees your time to think and add real value.

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Thank you Albert for inviting us to SAS for coffee and taking the time for this fun and informative interview!

 

Meet our Financial Math Alumni- Coffee Chat with Albert Hopping- Part 1

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Meet Albert Hopping, ERP- Manager of Risk Consulting at SAS Institute in Cary, North Carolina. Albert graduated from the Financial Math program in 2007. He is a Board Member and an active alumnus of our program. We were happy to meet with Albert for coffee at his office at SAS.

Part I: Education & Job Background:

1) Why did you decide to get a Master’s degree in Financial Mathematics from North Carolina State University?

Albert: That I might receive more wages. That is the short answer. I finished my undergraduate degree before this program existed. When I joined the program, I was working full time. I had been out of my undergraduate program for a few years and I ended up in a risk analytics team at a diversified energy company. At that point, I didn’t have a risk background and didn’t know much about the field. I was on the risk team looking around and I saw these quant guys programming in Matlab. It looked like fun to me and I thought that it was a cool job. I wanted to be a part of what they were doing, so I started helping them with their work as much as I could.

Eventually, it got to the point where I was doing this risk work a majority of my time. I told my manager that I should be moved to the quant job family. I was told that a master’s degree in Financial Mathematics was a prerequisite for the job. Not having the degree was a roadblock for me. I applied to the Financial Mathematics program that week and I am glad I did.

2) How did the program prepare you for your job?

Albert: I was already doing risk work; I was self-taught to a certain extent. This put me in a different position compared to most students, and I got different things out of the program than other people might have, as a result. Most students learn theory first and practice second. I started the program with the perspective of a practitioner. While in the program, I learned about models I used on the job. I used these tools at work, but I didn’t really know about stochastic partial differential equations. I used Black-Scholes, but I could not derive it.

What I received from the classes is a much deeper conceptual understanding and a firmer foundation from which to see my work. What I really took from this program is a fundamental, basic understanding of financial mathematics. I also learned new models and conceived great ideas to use in practice.

3) Please briefly describe your job, your job title, and your responsibility?

Albert: At SAS Institute, I am a Manager on the Risk Solution team of Professional Services & Delivery (PSD). Let me explain from the top down. PSD is the consulting, customization, and delivery arm of SAS. Many customers of SAS software want services, consulting, or even staff augmentation. PSD provides these services. We are the ones who go to the customer site and work with the customer to help them get the most benefit from our products. Our team within PSD specializes in the risk management domain. We work with all the risk solutions and provide consulting for all risk topics. Our team has about 20 members and is growing.

Within risk, I specialize in three industries Energy, Financial Services, and Healthcare. I am responsible for leading customer projects, providing industry and risk domain expertise to the sales teams, mentoring fellow team members, and most importantly providing value to the customer. Note that the views and opinions I express today are my own.

Part II: Analytic techniques

4) “Big Data” is a hot specialization in the field. Do you see this as a long term trend or something that might pass as a fad?

Albert: Big Data is definitely a long term trend. In fact, I would go beyond that; I would say it is going to be the new norm. It will progress to the point where big data is simply the paradigm. I will even extend that to unstructured data. Companies, who are not using big data and unstructured data to their advantage, are starting to fall behind. They are tomorrow’s luddites.

5) The trend of “Big Data” implies that people believe historical data can shed light on future prediction. However, this contradicts with “efficient market hypothesis” to some degree. What are your thoughts about this?

Albert: One of the things I would like to point out in terms of the “efficient market hypothesis,” is the irrationality in the market. A simple example comes to mind: technical traders discuss how a stock index will meet resistance or break through a barrier. But what are those points where the index meets resistance or breaks through? They are numbers with lots of zeroes on the end, round numbers. Why are those numbers important? They are only important because we tend to be emotional and we have ten fingers. I propose that if we had a different number of fingers we would use a different base for our number system. The round numbers where the stock index meets resistance would be different numbers.

Clearly, these barriers are irrational, as they are based on how many fingers we have. This means I cannot be a full believer in the “efficient market hypothesis.” The question remains, is all this historical data priced into the market already? To the extent that people are doing analytics on big data, perhaps yes. Was it priced in before? No. Was the data available? Mostly, but people could not convert the data into knowledge. It was impossible - until analytics on this big data was possible.

Now, we are in the place where something can be done because of the advancements in software and the physical hardware. Data can be restructured and put into use in the market. The fact that the data is available is clearly important, but prior to these advancements one could not glean actual insights. The data must be converted into information that helps those insights that yield a better price or a better model. Acting upon those insights is what makes the market more “efficient”.

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Stay tuned for Part 2 & follow Albert on twitter @SASQuant 

Join our new workshop- “Introduction to Financial Risk”

NC State's Financial Math program has partnered with 2004 Alumnus, Jonathan Leonardelli, to create a new workshop series "Introduction to Financial Risk" for all NC State students and faculty. The workshop is also opened to the public.

Students and faculty in Mathematics, Statistics, Economics, Finance, Operations Research, MBA and other related programs are welcome to join!

Here is what you will learn:

Risk Workshop Overview

Presenter information:

Jonathan Leonardelli, FRM, MFM

Jonathan Leonardelli, Risk Consultant at the Financial Risk Group, specializes in credit and market risk management. Over the course of his career he developed a diverse knowledge of retail banking risk as well as the technical skills needed to integrate risk assessment processes into a company’s business and technology infrastructure.

Jonathan’s career started with positions in the credit risk groups at Wells Fargo (Wachovia) and BB&T. In these positions, he developed expertise in acquisitions and portfolio risk management.  In his current position, Jonathan develops and implements processes that provide quantitative risk assessment and reporting capabilities for clients that include banks, hedge funds, and asset management companies.

Jonathan is an experienced presenter and author.  He is a certified SAS® Risk Dimensions Instructor. His papers in financial risk management covered topics such as the Dodd-Frank Act and its implications for risk professionals, as well as techniques for handling missing data. He has also authored a Webinar for the Insurance & Finance SAS® Users Group (IFSUG) regarding loss estimation using roll rate matrices.

Jonathan holds an Masters of Financial Mathematics from North Carolina State University and is a member of the Global Association of Risk Professionals (GARP).

FRM designation since 2010

SAS Certified Advanced Programmer for SAS 9

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Those interested- please contact Leslie Bowman, Director of Career Services- leslie_bowman@ncsu.edu 

Workshop begins Friday, September 5th 2014- registration deadline, August 28th

Stochastic models for option pricing- Jump-diffusion model

Background

The derivative pricing model developed by Black, Scholes and Merton is a huge success in financial engineering area. It says that there exists an arbitrage-free price for plain vanilla options and the investors can perfectly hedge them by constructing a self-finance portfolio. However, the empirical observation demonstrates that this model is not perfect. For one thing, two different options on the same underlying with the same expiry date but different strike prices can imply different volatility. Indeed, if one plots the implied volatility as a function of the strike price of an option, the curve is roughly smile-shaped. For another thing, the stock and foreign exchange prices are simply not log-normally distributed as the model assumes. And in fact, the actual distribution of the logs of asset price changes have fat tails. To cope with these problems, we need to introduce more sophisticated models.

Introduction

A big shortcoming of Black-Scholes model is that it assumes the asset price is a continuous function. But in reality, the stock market undergoes crash periodically. We, therefore, wish to permit the possibility of jumps in our model. In this post, we briefly discuss the jump-diffusion model presented by Merton. And in order to illustrate it, we first briefly discuss the properties of Poisson process.

Poisson process

The Poisson process with intensity lambda counts the number of jumps that occur at or before time t and its distribution is

1

Its increments are stationary and independent. The expectation of the increment is

2

The variance is the same as the mean

3

We define the compensated Poisson process as

4

Then M(t) is a martingale.

Now let Y1, Y2,… be a sequence of identically distributed random variables with mean Beta=EYi. We assume the random variables Y1, Y2,… are independent of one another and also independent of the Poisson process N(t). We define the compound Poisson process

5

Like the simple Poisson process, the increments of the compound Poisson process are stationary and independent, and the expectation is

6If we define the compensated compound Poisson process as

7then it is a martingale.

Asset driven by a Brownian motion and a compound Poisson process

In this section, the stock price will be modeled by the stochastic differential equation

8

where S is the stock price, W(t) is a Brownian motion, and Q(t) is a compound Poisson process. Lambda is the intensity of the jump and Beta is the expectation of the jump size Yi.

Under the original probability measure, the mean rate of return on the stock is a. We assume that the jump size yi > -1 for i = 1,…, M in order to guarantees that although the stock price can jump down, it cannot jump from a positive to a negative value or to zero. We begin with a positive initial stock price S(0), and the stock price is positive at all subsequent times.

By the property of Doleans-Dade exponential, one can find that the solution to the above SDE as

9

We now undertake to construct a risk-neutral measure. The probability measure is risk-neutral if and only if

10

This is equivalent to the equation

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which is the market price of risk equation for this model. Here the letters with tilt represent the corresponding variables in risk-neutral world. Obviously, there is no unique risk-neutral measure in this situation because one can find infinitely many combinations satisfying the market price of risk equation. One can choose a risk-neutral measure by matching the market. Here, we assume a certain risk-neutral measure is chosen.

Closed form formula for European call option

A jump-diffusion model with a continuous jump distribution was first treated by Merton, who considered the case in which one plus the jump size has a log-normal distribution

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For the next step, we need some notation. Define

13

where

14

and

15

is the cumulative standard normal distribution function. In other words,kappa(tau, x, r, sigma) is the standard Black-Scholes-Merton call price on a geometric Brownian motion with volatility sigma when the current stock price is x, the expiration date is tau time units in the future, the interest rate is r, and the strike price is K.

Now define tau = T t. We give the closed-form formula for the European Call option without proof

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With a little work, the price can be rewritten as

17

where

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These formulas were originally derived by Merton using PDE approach. Although the formula is an infinite series, it converges very fast and the first several terms can produce quite good approximation.

Jump-diffusion smile

In this part we discuss about the properties associated with the volatility smile generated by jump-diffusion model. It is straightforward that an option on a stock with a jump component is more valuable than an option on a stock without jump component. In fact, the effect of adding jumps can give rise to a heavy tail for the distribution of log stock price. Therefore, the out-of-money options become more valuable, a consequence leading to an implied-volatility smile.

The jump intensity lambda tilt controls the frequency of the happening of jumps. Increasing intensity makes the stock price more volatile, and thus the smile shape become steeper. On the other hand, the lower the jump intensity is, the flatter the smile would be. Also, the smile will be much sharper for short-term maturities. Over long time periods, the smile becomes more horizontal as the diffusive component of the model becomes dominant. See Figures 1 and 2.

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Figure 1 Jump-diffusion smiles for time horizons of one through three years. Spot is 110, jump intensity is 0.1, and jump size are log-normal distributed with mean equal to -1.

The distribution of jump size Y determines the shape of volatility smile. Using symmetric distribution of jumps will lead to a symmetric smile shape. While if we let jump size follows a log-normal distribution, like what we use in this post, the smile becomes downwards sloping. The parameter mu can affect the skewness of the smile. Usually, we pick mu < 0, which means the stock price more likely goes down when jump occurs. This causes a downwards sloping smile. If we let mu > 0, the smile becomes upwards sloping for large moneyness. See Figure 2 and 3.

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Figure 2 Jump-diffusion smiles for time horizons of one through three years. Spot is 110, jump intensity is 0.01, and jump size are log-normal distributed with mean equal to -1.

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Figure 3 Jump-diffusion smiles for time horizons of one through three years. Spot is 110, jump intensity is 0.01, and jump size are log-normal distributed with mean equal to 1.

I have implemented the final closed-form formula for pricing European options in an Excel add-in. One can use the functions in this library to check the shape of "volatility smile" generated by the model as what I did in the last part of the article. One can download this Excel add-in from the following link below. Add it into your Excel (only for windows system) it's free to use!- (by- Xiaohong Chen, May 2015 Graduate, Financial Math Intern, Career Ambassador)

 

Reference

[1] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, vol. 81, pp. 637-659, May/June 1973.
[2] R. C. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, vol. 4, pp. 141-183, Spring 1973.
[3] R. C. Merton, “Option Pricing When Underlying Stock Returns Are Discontinuous,” Journal of Financial Economics, vol. 3, pp. 125-44, March 1976.
[4] M. Joshi, The Concepts and Practice of Mathematical Finance, Cambridge University Press, 2003.
[5] J. C. Hull, Options, Futures, And Other Derivatives, Pearson Education Limited, 2012.
[6] S. E. Shreve, Stochastic Calculus for Finance II, Springer Science+Business Media, LLC, 2004.

 

Database trends in financial services that quants should know

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Recent trip to New York City included a small alumni meet-up and Data Summit 2014. At Data Summit 2014 we learned about several database trends in financial services well beyond the popular RDBMS (relational databases) including Hadoop Big Data Platforms, NoSQL, NewSQL, and in-memory databases.

Quants know SQL, and it's important for them to be aware of the above database trends and what's driving them in financial services - such as risk analytics and reporting, market data feeds, high frequency trading, regulation, among other use cases driving demand for high volume and scalable, specialized databases.  While many quants are proficient in programming, it's not reasonable to expect them to learn each programming language driving these technologies to access data (Erlang, Javascript, C#, Java, etc).  This is not unique to quants as we're seeing SQL enable wider adoption of the Hadoop Big Data Ecosystems.

Sumit Sarkar of Progress Software (Gold sponsor of our program) talks about how professionals such as those in quantitative finance can easily work with data in the growing landscape of highly specialized database technologies, MongoDB for example, using standard based SQL interfaces such as ODBC and JDBC.

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(Alumni Left to Right- Emmanuel Sanchez with Allianz; Director of Career Services, Leslie Bowman; Yoshi Funabashi with Credit Suisse; Brandon Blevins with Credit Suisse)

Keep a lookout for their  "Meet our Financial Math Alumni" interviews.

We will be back again in October, 2014- so all NYC alumni, plan for another fun gathering!

New Series- “Meet our Financial Math Alumni”- Coffee Chat with Jonathan Leonardelli

"Meet our Financial Math Alumni" is an up-close interview series with select Financial Math alumni to learn more about their career, experience and knowledge after receiving their Masters in Financial Math degree from NC State University. Alumni are important part of our program for many reasons. They provide support, vision and strategy to ensure the success of our program. They are role models and mentors for current students. They strengthen the reputation of the Financial Math program. They provide job leads and recruitment activity for students. Our alumni are intelligent and awesome! Thank you to those who participant in this series"- Leslie Bowman, Director of Career Services

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Meet Jonathan Leonardelli, FRM, Risk Consultant (Graduated 2004)

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Interview conducted and summarized by Yi Chao and Xiaohong Chen, Financial Math Interns, May 2015 Graduates

Jonathan is currently a Risk Consultant at Financial Risk Group. He is also one of the first students to graduate from NCSU’s Financial Mathematics program. We were honored to have the opportunity to interview him.

Part I: Education & Job Background

1) Interviewer: Why did you decide to get a Masters in Financial Math at NC State?

Jonathan: I had just moved here and was interested in changing careers. I wanted to find a program that combined mathematics and finance. As it happened, NC State was in the process of creating the Financial Mathematics program. Although the start of the program was still a couple years off, that time allowed me to get the necessary mathematics background I needed. Entering the program produced the exact result that I wanted: it gave the mathematics I need to do interesting work in the banking industry.

2) Interviewer: How did the program prepare you for your job?

Jonathan: The program really gave me the depth of math that I needed to work in the field of risk. It also taught me how to apply rigorous logic to a problem to help find a solution. Beyond this, though, I learned that life was filled with randomness. This randomness, as a result, causes the quantification of some metrics to be difficult.

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Part II: Analytic techniques

3) Interviewer: "Big Data" is a hot specialization in the field. Do you see this as long term trend or something that might pass as a fad?

Jonathan: It is definitely not a fad. In this day and age many actions we take, especially when using a piece of technology, is probably captured and stored in some database. Now, think about all those action and all the data that comes along with it. What is a company going to do with this data? They are going to improve their sales, improve their risk practice…the list goes on. Having skills to work with big data, to be able to find the relevant information and then integrate it into a model, is very useful.

4) Interviewer: The trend of “Big Data” implies that historical data can shed some lights on future prediction. However, this contradicts with “efficient market theory” to some degree. What are your thoughts about this?

Jonathan: I think concerns should always be involved when using historical data because the tacit assumption is that the future is going to behave like the past. That being said, there are ways to mitigate these concerns. For example, when we calibrate models one of the first things we do is test it with a different period of data to see if the model is robust. Sometimes we might use the model on data representative of a stressed scenario (i.e., a scenario that is uncommon but still possible) and see how the model performs. If it performs badly, we try to assess why that is. Are the parameter estimates wrong? Are different variables needed?

5) Interviewer: Does your company use stochastic models to predict interest rate? What kind of models are used?

Jonathan: To be honest, in my current job the main stochastic (i.e., diffusion based) models I have used are CIR (Cox-Ingersoll-Ross) and GBM (Geometric Brownian Motion) with the occasional jump-diffusion model thrown into the mix. Most of the models I have worked with recently are linear regression, logistic regression, and Markov chains.

6) Interviewer: In your area of specialization, what is your favorite method or model and why? Do you believe it is perfect?

Jonathan: Markov chains and their resulting transition matrices. This comes from the years when I worked in the banking industry. At a glance, the transition matrix tells you the behavior of different segments of accounts. Depending on how the states of the Markov chain are defined, the transition matrix can tell you: 1) The probability of going to default, 2) the probability of paying off, 3) the probability of curing, 4) the probability of moving across multiple states over a given time, etc.

The transition matrix is a great summary tool. Of course, it is not perfect. Always keep that in mind when you build a model. Even though the model looks pretty and deals well with the data – now – it is not perfect. It is an easy move from complacency, when the model is performing well during good times, to anxiety when the model is performing poorly during a financial crisis.

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Part III: Risk Management

7) Interviewer: How do the regulation policies enacted after crisis affect the behavior of your company?

Jonathan: The regulations have not impacted the behavior of our company. However as a risk consulting company, we have seen more requests from financial institutions asking us to help them comply with the regulations.

8) Interviewer: The goal of risk management is to achieve a balance between returns and risks. Thus, with a lot of capital and human resource spent, risk management may, to some extent, reduce a company’s profits. Driven by the motivation of maximizing the profits, will the companies pay enough attention for risk management?

Jonathan: I may be biased, given my chosen career path, but I think with the recent financial crisis still fresh in our memories as well as all the regulations that were created as a result of it, businesses will continue to pay enough attention to risk management. And, I think, it will be that way for a while.

Part IV: Suggestions & Advice

9) Interviewer: Any tips for those interested in getting into the field?

Jonathan: First, be comfortable with the idea of randomness. Randomness is uncertainty and uncertainty is risk. Second, companies do not only seek candidates that are good at math and programming. They also seek those candidates who can clearly present their ideas in writing and presentations. Third, get perspective from areas outside of mathematics. I strongly suggest taking business classes because it gives you a different view of a business. A company is multifaceted and does not solely revolve around models.

10) Interviewer: What courses do you recommend?

Jonathan: The courses in the Financial Math program are very good. Among them, I definitely think the probability course is the most important one. That course takes you deep into the world of randomness and, hopefully, makes you comfortable with it. If you have an option of taking a course on risk or financial regulation that would be good. I took econometrics as an elective and, more often than not, draw upon the math tools I learned from that class more than others. Another very good course I took, and have used frequently, is time series analysis.

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"It is a great experience to interview Jonathan. He is humorous and smart. We learned a lot when we talked with him. Thanks Jonathan for participating in our interview! We are sure that your answers will shed some light for those interested in Financial Mathematics!"- Yi Chao and Xiaohong Chen

 

A student’s interview experience- the benefits of planning and preparing for the big day!

Internship Interview Experience at a Financial Security Company

(Disclosure- this is a true interview story. This student received an offer and is currently working at this company. Her interview experience and interview format is typical but may not reflect all interview experiences. For privacy reason, the interviewee and company are made anonymous.)

I had an interview with the risk management model group of a financial security company. The main financial products of the company are mortgage loans insurance and long term care insurance.

The interview lasted two rounds, and each round covered two parts with two interviewers from the risk management model group. In the first round interview, the interviewer mainly asked about some questions ranging from mortgage loans, basic statistical knowledge of data mining to regression techniques and models. (Tip- Researching the employer was an important part of this round.)

Questions about mortgages loans referred to concept of premium, prepayment and interest rate. The interviewer introduced their mortgage product to me and I expressed some of my points of view about the product combined with financial terms that I learned in some related classes. (Tip- show employers your educational knowledge through related courses.)

In the basic statistical question part, I was asked about questions of distribution of certain scatter plots that were prepared by the interviewer. Besides, the interviewer asked me to come up with some fast data mining methods that can help a modeler quickly deal with data in an efficient way. (Tip- be prepared to show examples of your quantitative skills)

Most technical questions were focus on regression. The interviewer discussed with me two econometrics models that I had implemented before. Based on the discussion of certain regression models, the interviewer thoroughly asked questions about data cleaning, explanatory variables choosing and model modification. It was a nice progression since the interviewer guided me to take more practical problems into consideration in the process of model construction. (Tip- actively listen to the interviewer and be aware of the direction their conversation is heading, including tips they may give you.)

The second round of interview was an on-site visit to the company. During the second part of first round interview, the interviewer was interested in my interpretation of Logistic model application. I was also asked about basic SAS programming skills. Three interviewers interviewed me and gave me have a tour of the office. The SVP (Senior Vice President) of Risk Management introduced the team corporation of different groups in the division.

During the first part of the second round of interview, I had the opportunity to gather more details about the company’s business and culture, and had a nice communication with the interviewer about team contribution. All the questions were focused on the type of role that I could participate in the risk modeling team, and why I chose this company.

The Director and Modeler from the Risk Modeling team asked me to talk about some opinions on default probability model construction. Furthermore, they gave me concrete examples to show what kind of data that is usually dealt with and gave me chances to discuss practical techniques of data processing implemented by SAS programming. (Tip- be prepared to give  examples of your programming skills.)

The whole interview process was nice. The interviewers were willing to guide candidates to answer questions through practical problems solving techniques, come up with different solutions and opportunities for further discussion. The interview was a great way to communicate with professional people in the finance industry.

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Have you had an interview yet? If so, was your experience similar or different? Share your thoughts and comments.

Student’s view on Financial Math core courses at NC State

"Having taken many courses so far, Masters of Financial Math (MFM) students have discovered interesting and useful courses. Below are examples of a few core courses I have found important and useful."- Yizhou Chen, May 2015 Graduate

Statistical Theory:

Statistical Theory I & II is important in providing fundamental theory and formulas. In Statistical Theory II, we developed the probabilistic tools and language of mathematical statistics. The course describes basic probability theory, probabilistic models for a properties of random variables, common probability distributions for univariate and multivariate random variables, and sampling distributions and convergence theory. We learn description of discrete and absolutely continuous distributions, expected values, moments, moment generating functions, transformation of random variables, marginal and conditional distributions, independence, order-statistics, multivariate distributions, and concept of random sample.

The Statistical Theory classes are designed to provide the basic tools of statistical inference and prepare us to understand the foundations behind statistical inference. Thus, the knowledge enables us to formulate appropriate statistical procedures. Additionally we learn sufficient, ancillary, and complete statistics; Methods of finding estimators, including maximum likelihood; Mean squared error and unbiasedness; Hypothesis testing, including maximum likelihood; Mean squared error and unbiasedness; Hypothesis testing, including likelihood ratio; Power functions; Neyman-Pearson Lemma; Uniformly most powerful tests; Confidence intervals; Asymptotic properties of estimators and tests.

Asset Pricing:

Asset Pricing is a core course in the first semester of the Financial Math program. We gained a lot knowledge about finance from this course, especially for the students who have little knowledge about finance.  This course is an introduction to the pricing of assets. The emphasis is on the mathematical methods used to derive pricing formulas, and there is additional time devoted to explaining the major types of paper assets that can be priced with those methods. Real assets, such as factories and machines, also can be priced with the same methods. The goal of this course is to introduce us to the major types of asset prices and give us an understanding at an intuitive level of the relation between asset prices and the mathematics that governs their evolution.

The content in this course: Introduction to major fundamental assets (stocks and bonds), interest rates, and derivative assets, such as put and call options. Arbitrage theorem, present value, risk aversion, hedging, duration, properties of derivative assets, binomial trees, elementary stochastic calculus, Black-Scholes option pricing formula, implied volatility, capital asset pricing model. Emphasis on mathematical methods used to price derivative assets.

Probability and Stochastic Processes:

Probability and Stochastic Processes I: This course is set as an alternative course to Statistical Theory II. This course is more theoretical and the key point of this course is different from Statistical Theory I. In Statistical Theory I, we developed the probabilistic tools and language of mathematical statistics. Probability and Stochastic Processes describes basic probability theory, probabilistic models for and properties of random variables, common probability distributions for univariate and multivariate random variables, and sampling distributions and convergence theory. It is a modern introduction to Probability Theory and Stochastic Processes. The choice of material is motivated by applications to problems such as queueing networks, filtering and financial mathematics. Topics include: review of discrete probability and continuous random variables, random walks, markov chains, martingales, stopping times, erodicity, conditional expectations, continuous-time Markov chains, laws of large numbers, central limit theorem and large deviations.

Financial Mathematics:

Financial Mathematics- This is a core course in second semester, and challenging; some say difficult! Probability and Stochastic Processes and Asset Pricing courses are necessary to prepare us for Financial Mathematics class. Understanding the history of mathematics evolving over time as they are subjected to random shocks and knowledge of the mathematics of asset pricing are essential tools for this course.

Financial Mathematics course focuses on the basic mathematical tools for finance. In particular, we cover time value of the money, simple interest rate, bank discount rates, compound interest, ordinary annuities, extending ordinary annuities, amortization, sinking funds, perpetuities and capitalized costs.

Content of this course: Stochastic models of financial markets, No-arbitrage derivative pricing, discrete to continuous time models, Brownian motion, stochastic calculus, Feynman-Kac formula and tools for European options and equivalent martingale measures. We also learn about Black-Scholes formula, Hedging strategies and management of risk, Optimal stopping and American options, Term structure models and interest rate derivatives, and Stochastic volatility.

Monte Carlo Methods:

Monte Carlo Methods with Application to Financial Mathematics- This course requires some knowledge of programming. We use Matlab to write functions, apply appropriate control structures, and import and export data. We implement the methods mentioned in the other learning outcomes in Matlab. Matlab is utilized to visualize the results. The homework of this course may not be so difficult, but it takes a lot of time. Because of plenty use Matlab, we need take some pre-courses to prepare for it.

In this course we learn Monte Carlo (MC) methods for accurate option pricing, hedging and risk management. Modeling using stochastic asset models (e.g. geometric Brownian motion) and parameter estimation. Stochastic models, including use of random number generators, random paths and discretization methods (e.g. Euler-Maruyama method), and variance reduction."

By- Yizhou Chen, May 2015 Graduate, Career Ambassador & Financial Math Intern

Learn more about NC State Masters of Financial Math.

Meet Xun Ma- Career Ambassador of the Week

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"My name is  Xun Ma (May 2015 Graduate), and come from a small city in the southeast of China, Guiyang. As a first year student in Financial Mathematics program at North Carolina State University, I got an awesome opportunity to be an Ambassador of the program.

Before I came to the Financial Mathematics program, I was majored in Econometrics. As a Chinese student, I found that I learned a lot through the work experience as an Ambassador. The Ambassador is a role not only about leadership, but also a role about professionalism. This is a good way to experience professional environment in the United States. Within few months in the role, I had the opportunity to have close communication with professionals in financial industry and help advisors to prepare board meetings and career fairs. All of these professional events fulfill the rest of my time out of academic study.

My personal interest is to apply mathematical skills in model construction in order to solve practical problems. In the short run, I plan to be a risk modeler. So far, I enjoy learning related numerical skills and programming skills based on solid theoretical knowledge in quantitative finance. I have implemented my quantitative skills in several projects that are mainly focus on explaining the relationship between interest rate spread and sovereign debt crisis.

More importantly, my Ambassador role provides extra resources to help me improve my communication skills and opportunities to introduce myself to a large range of working professionals from different companies. All of these experiences give me passion and confidence to pursue my career goal."- Xun Ma