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Indian Institute of Technology Kanpur

Probability and Stochastics for Finance

Indian Institute of Technology Kanpur and NPTEL via Swayam

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Overview

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This course provides the minimum mathematical requirements to study mathematical finance or more precisely the pricing of financial derivativesPRE-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.

Syllabus

Week 1:
Fundamentals of Interest RateFixed income securitiesTerm structure of Interest rate-ITerm structure of Interest rate-IIOptimization problems in Finance
Week 2:
Crash course on Karush-Kuhn-Tucker ConditionsMean Variance Portfolio OptimizationMarketing Model & Related IssuesThe Capital Asset Pricing Model-IThe Capital Asset Pricing Model-II
Week 3:
The Basics of Financial Markets & Financial DerivativesBinomial Trees and ArbitragePricing Options using Binomial Trees-IPricing Options using Binomial Trees-IIGirsanov's Theorem
Week 4:
Black Scholes Formula:The Risk Neutral ApproachMore on Black Scholes FormulaDividend Paying StocksPricing Forwards & Futures-IPricing 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
Martingales
Brownian Motion

Week 7:
Ito Integral
Ito Calculus

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

Taught by

Joydeep Dutta

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Reviews

5.0 rating, based on 1 Class Central review

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  • Anonymous
    Got an opportunity to do his classroom course as a part of my college curriculum at IIT Kanpur. Extremely liked the course and the course serves as a great bridge for people who have not much idea about the maths behind it.
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