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Physics of Finance


Admission Requirements

No particular requirement for students having successfully completed basic 1st- and 2nd-year BSc courses in physics, astronomy or mathematics. Students with a different background are advised to seek prior interaction with the instructors.


This course introduces how physics and physics concepts play a role in the dynamics of financial markets. At its core is the equivalence between the heat equation and the Black- Scholes equation for option pricing. We build on this to explore the dynamics of financial markets, volatility and the problems of pricing of financial derivatives. We will highlight both commonalities and differences between physics and finance questions. During the lab sessions, students will have a chance to implement gradually more complex derivative pricing models and use their output to trade on a simulated exchange.

Lecture 1: Introduction to Financial Markets & Instruments.
Lecture 2: From the Heat Equation to Black-Scholes and Option Pricing.
Lecture 3: Greeks; its physical interpretation, characteristics and dynamics.
Lecture 4: Stochastic volatility and the Heston model.
Lecture 5: Local volatility; American Style Options.
Lecture 6: Exotic options and summary.

Course objectives

Understanding financial markets and how physics can play a crucial role in modelling financial derivatives and price them.

Transferable skills

Scientific curiousity, creating connections among different contexts and disciplines, thinking out of the box, being able to formulate hypotheses about problems for which one has no prior knowledge, abstraction and generalization in a multidisciplinary context.


See timetable in Brightspace
You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different

Mode of instruction

See Brightspace

Assessment method

Students will be evaluated based on the homework assignments, not an exam. Completing all the assignments will eventually lead to a working pricing/trading algorithm, but each intermediate result will be important and judged more on the understanding of concepts rather than on the details of implementation. Having a clean and fully integrated setup might award some bonus points.

Reading list

Slides and other notes/material (will be made available on Brightspace).


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.


Lecturers: Dr. D. Garlaschelli
Artur Swiech
Andrea Fontanari
Robbert Pullen