Probability and Stochastics for Finance

By Prof. Joydeep Dutta   |   IIT Kanpur
Learners enrolled: 925
This course provides the minimum mathematical requirements to study mathematical finance or more precisely the pricing of financial derivatives

PRE-REQUISITE: Mathematics should be at least a course among the minor subjects.
INTENDED AUDIENCE:  Senior UG or PG students in Mathematics, Physics,  Economics or Finance with mathmatics as one of the subjects.
Professionals from the finance industry.
INDUSRTY SUPPORT:  Any financial firms like Goldman Sachs, Investment Department of Banks would be interested.
Course Status : Completed
Course Type : Core
Duration : 8 weeks
Category :
  • Mathematics
Credit Points : 2
Level : Undergraduate/Postgraduate
Start Date : 24 Jan 2022
End Date : 18 Mar 2022
Enrollment Ends : 07 Feb 2022
Exam Date : 27 Mar 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1:
Fundamentals of Interest Rate
Fixed income securities
Term structure of Interest rate-I
Term structure of Interest rate-II
Optimization problems in Finance

Week 2:

Crash course on Karush-Kuhn-Tucker Conditions
Mean Variance Portfolio Optimization
Marketing Model & Related Issues
The Capital Asset Pricing Model-I
The Capital Asset Pricing Model-II

Week 3:
The Basics of Financial Markets & Financial Derivatives
Binomial Trees and Arbitrage
Pricing Options using Binomial Trees-I
Pricing Options using Binomial Trees-II
Girsanov's Theorem

Week 4:
Black Scholes Formula:The Risk Neutral Approach
More on Black Scholes Formula
Dividend Paying Stocks
Pricing Forwards & Futures-I
Pricing Forwards & Futures-II

Week 5:
Basic Probability
Interesting problems in Probability
Random variables, Distribution Functions and Independence
Chebyshev's Inequality, Borel-Cantelli Lemmas and related issues
Law of Large Numbers and Central Limit Theorem

Week 6:
Conditional Expectation
Brownian Motion

Week 7:
Ito Integral
Ito Calculus

Week 8:
Ito Integral in Higher Dimensions
Applications of Ito Integral
Black-Scholes Formula

Books and references


Instructor bio

Prof. Joydeep Dutta

IIT Kanpur
Prof.Joydeep Dutta is currently a Professor of Economics at the Department of Humanities and Social Sciences, IIT Kanpur. He was previously a Professor at the Department of Mathematics and Statistics at IIT Kanpur. His reseach interest primarily lies in optimization though he loves mathematics as a whole.

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:  27 March 2022  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 6 assignments out of the total 8 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 Kanpur. 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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