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.
Probability and Stochastics for Finance
Indian Institute of Technology Kanpur and NPTEL via Swayam
This course may be unavailable.
Overview
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
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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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.
