Mathematical Finance

By Prof. N. Selvaraju, Prof. Siddhartha Pratim Chakrabarty   |   IIT Guwahati
Learners enrolled: 2074
The course on ‘Mathematical Finance’ gives an introduction to this interesting and growing area. In particular, the course will cover two Nobel-prize winning frameworks, namely portfolio theory and the option pricing theory.

INTENDED AUDIENCE: Students at advanced undergraduate and postgraduate level in Mathematics, Statistics and allied areas as well as students of Engineering and Management interested in this field.
PREREQUISITES:          Background in basics of probability theory
INDUSTRY SUPPORT:    Finance Industry
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Start Date : 14 Sep 2020
End Date : 04 Dec 2020
Exam Date : 20 Dec 2020
Enrollment Ends : 25 Sep 2020
Category :
  • Mathematics
Level : Undergraduate/Postgraduate

Course layout

Week 1: Introduction to financial markets, financial instruments, bonds, stocks and financial derivatives.
Week 2: Time value of money, simple and compound interest rate, net present value, internal rate of return and annuities.
Week 3: Markowitz portfolio theory, risk and return, two and multi asset portfolio theory, efficient frontier.
Week 4: Capital Asset Pricing Model and portfolio performance analysis.
Week 5: No arbitrage principle, pricing of forwards and futures, properties of options. 
Week 6: Derivative pricing by replication in binomial model.
Week 7: Discrete probability spaces, filtration, conditional expectation
Week 8: Discrete time martingales, Markov chain, risk-neutral pricing in binomial model for European and American derivatives.
Week 9: General probability spaces, conditional expectation, Brownian motion.
Week 10: Ito integral, Ito formula, Girsanov’s theorem, martingale representation theorem, stochastic differential equation.
Week 11: Black-Scholes-Merton (BSM) model, pricing of European derivatives in BSM framework.
Week 12: Valuation of European options in BSM model, BSM formula, BSM partial differential equation, hedging, model completeness, fundamental theorems of asset pricing.

Books and references

1.  J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice-Hall of India, 2007.          
2.  M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, Springer, 2005.
3.  S. Shreve, Stochastic Calculus for Finance, Volume 1, Springer, 2004.
4.  S. Shreve, Stochastic Calculus for Finance, Volume 2, Springer, 2004.
5.  A.O. Petters and X. Dong, An Introduction to Mathematical Finance with Applications, Springer, 2016.

Instructor bio

Prof. N. Selvaraju

Prof. Selvaraju has more than ten years of teaching experience (in addition to research experience) in the areas of financial mathematics, financial engineering, stochastic calculus and portfolio theory and has offered several courses to the B.Tech. (Mathematics and Computing) and M.Sc. (Mathematics and Computing) students of IIT Guwahati.

Prof. Siddhartha Pratim Chakrabarty

IIT Guwahati
Prof. Chakrabarty has more than ten years of teaching experience (in addition to research experience) in the areas of financial engineering, computational finance, portfolio theory and financial risk management and has offered several courses to the B.Tech. (Mathematics and Computing) and M.Sc. (Mathematics and Computing) students of IIT Guwahati.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 20 December 2020 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Guwahati .It will be e-verifiable at nptel.ac.in/noc

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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