Financial Derivatives and Partial Differential Equations

In addition to the basic entry requirements, knowledge equivalent to the course Options and Mathematics (MMG810) or a total of 90 credits in mathematics and mathematical statistics is required.

Probability and measure theory. Brownian motion and stochastic calculus. The Ito‐Doeblin and Feynman‐Kac formulas. Girsanovʹs theorem. Risk‐neutral pricing. Self‐financing portfolio strategies and arbitrage. Martingale representation and complete markets. The Black‐Scholes model. Puts and calls. Several underlying assets. Path‐dependent options. Forward and futures contracts, barrier options, up-and-out call, change of numeraire, foreign and domestic risk-neutral measures, forward measures.

On successful completion of the course the studentwill be able to:

• master applications of the Ito‐Doeblin and Feynman‐Kac formulas to option pricing,
• account for risk‐neutral pricing,
• derive the Black‐Scholes differential equationfor the price of a simple European derivative when there are several underlying stocks,
• price European barrier options in the Black‐Scholes model,
• use domestic and foreign risk neutral measures to price derivatives on currencies.

The course is assessed by means of a written examination at the end of the course. During the course, there may be components that award bonus marks towards the examination. Examples of such components include quizzes, assignments or laboratory sessions. Information regarding the current course intake is provided via the course website.

If a student who has failed the same assessment component twice wishes to change examiner for the next examination session, such a request shall be granted unless there are specific reasons to the contrary (Chapter 6, Section 22 of the Higher Education Act).

If a student has received notification of educational support from the University of Gothenburg, including a recommendation for an adapted examination and/or an adapted form of assessment, the examiner may, provided this is compatible with the course’s learning outcomes and does not require unreasonable resources, decide to grant the student an adapted examination and/or an adapted form of assessment.

If a course has been discontinued or has undergone a major change, the student shall be offered at least two examination opportunities in addition to the standard examination opportunity. These opportunities shall be spread over a period of at least one year, but no longer than two years after the course has been discontinued or changed.

If a student has been notified that they meet the requirements to be a student at the Riksidrottsuniversitetet (RIU student), the examiner is entitled to decide on adjustments to the examination, provided this is done in accordance with the Local Regulations concerning RIU students at the University of Gothenburg.

The grading scale comprises: Pass with Distinction (VG), Pass (G) and Fail (U).

The course is evaluated with an anonymous questionnaire and/or a discussion with the student representatives. The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.

The department has previously also offered the courses Financial derivatives and stochastic analysis MMA710, and Financial Derivatives and Partial Differential Equations MMA712. It is not permitted to register for or take examinations in more than one of these three courses.