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DPhil (PhD) studies in Mathematical Finance @ Oxford

The Mathematical and Computational Finance Group (MCFG) at Oxford is one of the largest and most dynamic research environments in mathematical finance in the world.

We combine core mathematical expertise with interdisciplinary approach. We foster lively interactions between researchers coming from different backgrounds and a truly impressive seminar programme, all this within one of the world's top universities, singular through its tradition and unique environment.

If you are passionate about mathematics and research and want to pursue a DPhil in Financial Mathematics, Oxford simply offers one of the best and most exciting places to do it!

 Research Topic and Supervisor Allocation

We welcome students with their own particular ideas of research topic as well as students with a broad interest in the field of Mathematical Finance. You have an opportunity to tell us about your research passions, and indicate potential supervisors, in your application form. This will be followed up during the interview.

In light of this, if you are offered a place, an appropriate supervisor will be proposed prior to your arrival in Oxford. However, there can be some flexibility over this once you arrive.  Keeping with the Oxford tradition, we offer our students independence and respect as early researchers, and always aim to match students with the most appropriate supervisors.

Outstanding students with a strong background in analysis, probability and data science are welcome to apply for our DPhil program. Each year we receive a large number of excellent applications. The selection process is extremely competitive and we can only admit a handful of candidates each year.

In order to apply for DPhil studies in Mathematical & Computational Finance, please indicate your interest in Mathematical and Computational Finance on your application form. Selected applicants will be invited for an interview -- either in person or by video call.

For general information on DPhil please consult our  Doctor of Philosophy (DPhil) admissions pages .

For the CDT Mathematics of Random Systems please consult our  the CDT website .

Or please contact  @email .

Funding for DPhil students is available from a variety of sources. Please note that some funding opportunities have deadlines: it is advised to apply before the deadline in order to maximise your chances of receiving funding.

Funding is also available through the  Centre for Doctoral Training in Mathematics of Random Systems . To apply for this program please How to Apply .

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• PhD in Mathematical Finance

The PhD in Mathematical Finance is for students seeking careers in research and academia. Doctoral candidates will have a strong affinity for quantitative reasoning and the ability to connect advanced mathematical theories with real-world phenomena. They will have an interest in the creation of complex models and financial instruments as well as a passion for in-depth analysis.

Learning Outcomes

The PhD curriculum has the following learning goals. Students will:

• Demonstrate advanced knowledge of literature, theory, and methods in their field.
• Be prepared to teach at the undergraduate, master’s, and/or doctoral level in a business school or mathematics department.
• Produce original research of quality appropriate for publication in scholarly journals.

After matriculation into the PhD program, a candidate for the degree must register for and satisfactorily complete a minimum of 16 graduate-level courses at Boston University. More courses may be needed, depending on departmental requirements.

PhD in Mathematical Finance Curriculum

The curriculum for the PhD in Mathematical Finance is tailored to each incoming student, based on their academic background. Students will begin the program with a full course load to build a solid foundation in not only math and finance but also the interplay between them in the financial world. As technology plays an increasingly larger role in financial models, computer programming is also a part of the core coursework.

Once a foundation has been established, students work toward a dissertation. Working closely with a faculty advisor in a mutual area of interest, students will embark on in-depth research. It is also expected that doctoral students will perform teaching assistant duties, which may include lectures to master’s-level classes.

Course Requirements

The minimum course requirement is 16 courses (between 48 and 64 credits, depending on whether the courses are 3 or 4 credits each). Students’ course choices must be approved by the Mathematical Finance Director prior to registration each semester. The following is a typical program of courses.

• GRS EC 701 Microeconomic Theory
• GRS MA 711 Real Analysis
• GRS MA 779 Probability Theory I
• QST FE 918 Doctoral Seminar in Finance
• GRS EC 703 Advanced Microeconomic Theory
• GRS MA 776 Partial Differential Equations
• GRS MA 781 Probability Theory 2
• QST FE 920 Advanced Capital Market Theory
• GRS EC 702 Macroeconomic Theory
• GRS MA 783 Advanced Stochastic Processes
• QST MF 850 Advanced Computational Methods
• QST MF 922 Advanced Mathematical Finance
• GRS EC 704 Advanced Microeconomic Theory
• GRS MA 751 Statistical Machine Learning
• QST MF 810 FinTech Programming
• QST MF 921 Topics in Dynamic Asset Pricing

Additional Requirements

Qualifying examination.

Students must appear for a qualifying examination after completion of all coursework to demonstrate that they have:

• acquired advanced knowledge of literature and theory in their area of specialization;
• acquired advanced knowledge of research techniques; and
• developed adequate ability to craft a research proposal.

Guidelines for the examination are available from the departments. Students who do not pass either the written and/or oral comprehensive examination upon first try will be given a second opportunity to pass the exam. Should the student fail a second time, the student’s case will be reviewed by the Mathematical Finance Program Development Committee (MF PDC), which will determine if the student will be withdrawn from the PhD program. In addition, the PhD fellowship (if applicable) of any student who does not pass either the written and/or oral comprehensive examination after two attempts will be suspended the semester after the exam was attempted.

Dissertation

Following successful completion of the qualifying examination, the student will develop a research proposal for the dissertation. The final phase of the doctoral program is the completion of an approved dissertation. The dissertation must be based on an original investigation that makes a substantive contribution to knowledge and demonstrates capacity for independent, scholarly research.

Doctoral candidates must register as continuing students for DS 999 Dissertation, a 2-credit course, for each subsequent regular semester until all requirements for the degree have been completed. PhD students graduating in September are required to register for Dissertation in Summer Session II preceding graduation.

Academic Standards

Time limit for degree completion.

After matriculation into the PhD program, a candidate for the degree must meet certain milestones within specified time periods (as noted in the table below) and complete all degree requirements within six years of the date of first registration. Those who fail to meet the milestones within the specified time, or who do not complete all requirements within six years, will be reviewed by the PhD PDC and may be dismissed from the program. A Leave of Absence does not extend the six-year time limit for degree completion.

Performance Review

The Mathematical Finance Program Development Committee will review the progress of each doctoral candidate. Students must maintain a 3.30 cumulative grade point average in all courses to remain in good academic standing. Students who are not in good academic standing will be allowed one semester to correct their status. Prior to the start of the semester, the student must submit a letter to the Faculty Director (who will forward it to the PDC) explaining why the student has fallen short of the CGPA requirement and how the student plans to correct the situation. Failure to increase the CGPA to acceptable levels may result in probation or withdrawal from the program, at the discretion of the PhD Program Development Committee (PDC).

Graduation Application

Students must submit a graduation application at least seven months before the date they expect to complete degree requirements. It is the student’s responsibility to initiate the process for graduation. The application is available online and should be submitted through the Specialty Master’s & PhD Center website for graduation in January, May, or August.

If graduation must be postponed beyond the semester for which the application is submitted, students should contact the Specialty Master’s & PhD Center to defer the date. If students wish to postpone their graduation date past the six-year time limit for completion, they must formally petition the PhD Program Development Committee (PDC) for an extension. The petition, which must include the reason(s) for the extension as well as a detailed timetable for completion, is subject to departmental and PDC approval.

PhD degree requirements are complete only when copies of the dissertation have been certified as meeting the standards of Questrom School of Business and have been accepted by Mugar Memorial Library.

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A pioneer in its field, the Financial Mathematics Program offers 15 months of accelerated, integrated coursework that explores the deep-rooted relationship that exists between theoretical and applied mathematics and the ever-evolving world of finance. Their mission is to equip students with a solid foundation in mathematics, and in doing so provide them with practical knowledge that they can successfully apply to complicated financial models. Financial Mathematics students become leaders in their field; program alumni have gone forth to find success at companies like JP Morgan, UBS, and Goldman Sachs. Read more

Why Study for a Mathematical Finance PhD?

I was emailed by a reader recently asking about mathematical finance PhD programs and the benefits of such a course. If you are considering gaining a PhD in mathematical finance, this article will be of interest to you.

If you are currently near the end of your undergraduate studies or are returning to study after some time in industry, you might consider starting a PhD in mathematical finance. This is an alternative to undertaking a Masters in Financial Engineering (MFE), which is another route into a quantitative role. This article will discuss exactly what you will be studying and what you are likely to get out of a PhD program. Clearly there will be differences between studying in the US, UK or elsewhere. I personally went to grad school in the UK, but I will discuss both UK and US programs.

Mathematical finance PhD programs exist because the techniques within the derivatives pricing industry are becoming more mathematical and rigourous with each passing year. In order to develop new exotic derivatives instruments, as well as price and hedge them, the financial industry has turned to academia. This has lead to the formation of mathematical finance research groups - academics who specialise in derivatives pricing models, risk analysis and quantitative trading.

Graduate school, for those unfamiliar with it, is a very different experience to undergraduate. The idea of grad school is to teach you how to effectively research a concept without any guidance and use that research as a basis for developing your own models. Grad school really consists of a transition from the "spoon fed" undergraduate lecture system to independent study and presentation of material. The taught component of grad school is smaller and the thesis component is far larger. In the US, it is not uncommon to have two years of taught courses before embarking on a thesis (and thus finding a supervisor). In the UK, a PhD program is generally 3-4 years long with either a year of taught courses, or none, and then 3 years of research.

A good mathematical finance PhD program will make extensive use of your undergraduate knowledge and put you through graduate level courses on stochastic analysis, statistical theory and financial engineering. It will also allow you to take courses on general finance, particularly on corporate finance and derivative securities. When you finish the program you will have gained a broad knowledge in most areas of mathematical finance, while specialising in one particular area for your thesis. This "broad and deep" level of knowledge is the hallmark of a good PhD program.

Mathematical Finance research groups study a wide variety of topics. Some of the more common areas include:

• Derivative Securities Pricing/Hedging: The technical term for this is "financial engineering", as "quantitative analysis" now encompasses a wide variety of financial areas. Some of the latest research topics include sophisticated models of options including stochastic volatility models, jump-diffusion models, asymptotic methods as well as investment strategies.
• Stochastic Calculus/Analysis: This is more of a theoretical area, where the basic motivation stems from the need to solve stochastic differential equations. Research groups may look at path-dependent PDEs, functional Ito calculus, measure theory and probability theory.
• Fixed Income Modeling: Research in this area centres on effectively modelling interest rates - such as multi-factor models, multi-curve term structure models as well as interest rate derivatives such as swaptions.
• Numerical Methods: Although not always strictly related to mathematical finance, there is a vast amount of university research carried out to try and develop more effective means of solving equations numerically (i.e. on the computer!). Recent developments include GPU-based Monte Carlo solvers, more efficient matrix solvers as well as Finite Differences on GPUs. These groups will almost certainly possess substantial programming expertise.
• Market Microstructure/High-Frequency Modeling: This type of research is extremely applied and highly valued by funds engaged in this activity. You will find many academics consulting, if not contracting, for specialised hedge funds. Research areas include creating limit order market models, high frequency data statistical modelling, market stability analysis and volatility analysis.
• Credit Risk: Credit risk was a huge concern in the 2007-2008 financial crisis and many research groups are engaged in determining such "counterparty risks". Credit derivatives are still a huge business and so a lot of research goes into collateralisation of securities as well as pricing of exotic credit derivatives.

These are only a fraction of the total areas that are studied within mathematical finance. The best place to find out more about research topics is to visit the websites of all the universities which have a mathematical finance research group, which is typically found within the mathematics, statistics or economics faculty.

The benefits of undertaking a PhD program are numerous:

• Employment Prospects: A PhD program sets you apart from candidates who only possess an undergraduate or Masters level ability. By successfully defending a thesis, you have shown independence in your research ability, a skill highly valued by numerate employers. Many funds (and to a lesser extent, banks) will only hire PhD level candidates for their mathematical finance positions, so in a pragmatic sense it is often a necessary "rubber stamp". In investment banks, this is not the case so much anymore, as programming ability is generally prized more. However, in funds, it is still often a requirement. Upon being hired you will likely be at "associate" level rather than "analyst" level, which is common of undergraduates. Your starting salary will reflect this too.
• Knowledge: You will spend a large amount of time becoming familiar with many aspects of mathematical finance and derivatives theory. This will give you a holistic view into the industry and a more transferable skill set than an undergraduate degree as you progress up the career ladder. In addition, you will have a great deal of time to learn how to program models effectively (without the day-to-day pressure to get something implemented any way possible!), so by the time you're employed, you will be "ahead of the game" and will know best practices. This aspect is down to you, however!
• Intellectual Prospects: You are far more likely to gain a position at a fund after completing a PhD than without one. Funds are often better environments to work in. There is usually less stress and a more relaxed "collegiate" environment. Compare this to working on a noisy trading floor, where research might be harder to carry out and be perceived as less important.

I would highly recommend a mathematical finance PhD, so long as you are extremely sure that a career in quantitative finance is for you. If you are still unsure of your potential career options, then a more general mathematics, physics or engineering PhD might be a better choice.

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Finance Department | PhD Program

Phd program.

Our faculty, ranked #1 worldwide based on publications in top finance journals (ASU Finance Rankings), consists of more than 30 researchers who study all major areas of finance, making it one of the largest finance faculty in the country. Stern’s finance faculty is highly rated in terms of research output, and faculty members sit on the editorial boards of all major finance journals.

The finance department offers an exceptionally large range of courses devoted exclusively to PhD students. Apart from core PhD courses in asset pricing and corporate finance, students can choose from a range of electives such as household finance, macro-finance, and financial intermediation. PhD students also enjoy the benefits of Stern’s economics department, NYU’s economics department in the Graduate School of Arts and Science (GSAS), and the Courant Institute of Mathematics.

Graduates of Stern’s Finance PhD program have been placed at leading research institutions such as Harvard, MIT, Chicago, Stanford, Wharton, Yale, and UCLA.

Holger Mueller , Finance PhD coordinator

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Wharton’s PhD program in Finance provides students with a solid foundation in the theoretical and empirical tools of modern finance, drawing heavily on the discipline of economics.

The department prepares students for careers in research and teaching at the world’s leading academic institutions, focusing on Asset Pricing and Portfolio Management, Corporate Finance, International Finance, Financial Institutions and Macroeconomics.

Wharton’s Finance faculty, widely recognized as the finest in the world, has been at the forefront of several areas of research. For example, members of the faculty have led modern innovations in theories of portfolio choice and savings behavior, which have significantly impacted the asset pricing techniques used by researchers, practitioners, and policymakers. Another example is the contribution by faculty members to the analysis of financial institutions and markets, which is fundamental to our understanding of the trade-offs between economic systems and their implications for financial fragility and crises.

Faculty research, both empirical and theoretical, includes such areas as:

• Structure of financial markets
• Formation and behavior of financial asset prices
• Banking and monetary systems
• Corporate control and capital structure
• Saving and capital formation
• International financial markets

Candidates with undergraduate training in economics, mathematics, engineering, statistics, and other quantitative disciplines have an ideal background for doctoral studies in this field.

Effective 2023, The Wharton Finance PhD Program is now STEM certified.

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Finance Requirements

I. preparation.

The study of financial economics requires a grasp of several types of basic mathematics. Students must enter with or very quickly acquire knowledge of the concepts and techniques of:

It is strongly advised that students without a strong and recent background in calculus, linear algebra, or statistics come to Stanford in June to take courses to strengthen any weak areas.

Computer programming skills are necessary in coursework (as early as the first quarter of the first year) and in research. If students do not have adequate computer programming skills, they may wish to take a computer programming course before they arrive at Stanford, or take an appropriate Stanford computer science course while here.

II. Course Requirements

All required courses must be taken for a grade (not pass/fail or credit/no credit). Exceptions are made if the required course is offered pass/fail or credit/no credit only. Each course must be passed with a grade of P or B- or better. Substitutions of required courses require approval from the faculty liaison. Waiving a course requirement based on similar doctoral level course completed elsewhere requires the approval of the course instructor, faculty liaison, and the PhD Program Office.

III. Practicum

Students are required to sign up for either a research or teaching practicum each quarter of enrollment. Below is a description of the practicum requirements for Finance students.

During the student’s first year, the student will be assigned each quarter to work with a different faculty member. This assignment will involve mentoring and advising from the faculty member and RA work from the student. The purpose of new assignments each quarter is to give the student exposure to a number of different faculty members.

In subsequent years, the practicum will take the form of a research or teaching mentorship, where the student is expected to provide research or teaching support under the guidance and advice of a faculty member. Faculty assignments here will be made through informal discussions between faculty and students, and may be quarterly, or for the entire year.

For students of all years, one requirement to satisfy the practicum is that students regularly attend the Finance seminar. The only exception to this will be if there is a direct and unavoidable conflict between the seminar and necessary coursework.

IV. Summer Research Papers

All students in all years are expected to complete a research paper over the summer, and present this paper in the Fall quarter. A draft of this research paper should be submitted by the end of September to the field liaison. Students can continue to work on and improve their paper up to their presentation.

For students completing their first year, the summer paper should demonstrate the mastery of a specific area in the literature together with the early development of a research idea in this area. The student will be expected to present this paper to a gathering of three Finance faculty members of the student’s choosing in October.

In all years after the first year, the summer research paper should be a well-developed research paper. (Well-developed does not mean completed – research is always presented as work in progress. Rather, it means that the work shows enough progress and development to merit a seminar presentation.) Students will then present their papers to the overall Finance faculty and PhD student body in scheduled talks over the Fall quarter. Student presentations will typically be 45 minutes, save for job market paper presentations, which will be a full hour and a half.

A passing grade on the paper at the end of the second year is one requirement for admission to candidacy. More generally, these presentations throughout all years will be a primary manner that faculty who are not advising the student become familiar with the student’s work, and will play a crucial role in the assessment of the student’s academic progress.

V. Field Exam

Students take the field exam in the summer after the first year. Material from the field exam will be based on required first year coursework. This includes required finance courses, as well as the required microeconomic and econometric classes. The primary purpose of the exam is to ascertain that students have learned the introductory material that is a necessary foundation for understanding and undertaking research in the field. Additionally, studying for the field exam will give students the opportunity to review and synthesize material across all their different first year courses. Students may be asked to leave the program if they fail the field exam, or may be allowed to retake the exam at the Faculty’s discretion. Students who fail the field exam two times will be required to leave the program.

VI. Teaching Requirement

One quarter of course assistantship or teaching practicum. This requirement must be completed prior to graduation.

VII. Finance Oral Exam

The finance oral exam takes place at the end of the spring quarter of the second year, in early June.

At the beginning of the spring quarter of the second year, the student meets with the liaison to determine three finance faculty members who will administer the exam. The student then meets with the selected faculty examiners to discuss a set of topics that will be covered in the finance oral exam. These topics will generally be chosen from coverage in the Finance PhD classes. An important component of the exam involves the student identifying a particular research area to discuss at the exam. The student will be expected to discuss major results in the literature related to this area and to identify important unresolved questions that need to be addressed. In addition the student will be expected to discuss how one or more of these questions might be addressed either theoretically or empirically. This discussion can be viewed as a preliminary step towards identifying the research project of the second year paper. The results from the finance oral exam plus the result from the second-year summer research paper (presented in the fall of 3rd year) and overall performance in the program are weighed in the decision to admit to candidacy.

VIII. Candidacy

Admission to candidacy for the doctoral degree is a judgment by the faculty of the student’s potential to successfully complete the requirements of the degree program. Students are required to advance to candidacy by September 1 before the start of their fourth year in the program.

IX. University Oral Exam

The university oral examination is a defense of the dissertation work in progress. The student orally presents and defends the thesis work in progress at a stage when it is one-half to two-thirds complete. The oral examination committee tests the student on the theory and methodology underlying the research, the areas of application and portions of the major field to which the research is relevant, and the significance of the dissertation research. Students are required to successfully complete the oral exams by September 1 before the start of their fifth year in the program.

X. Doctoral Dissertation

The doctoral dissertation is expected to be an original contribution to scholarship or scientific knowledge, to exemplify the highest standards of the discipline, and to be of lasting value to the intellectual community. The Finance faculty defer to the student’s Dissertation Reading Committee to provide general guidelines (e.g., number of chapters, length of dissertation) on the dissertation.

Typical Timeline

Years one & two.

• Field Requirements
• Directed Reading & Research
• Advancement to Candidacy
• Formulation of Research Topic
• Annual Evaluation
• Continued Research

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