ABOUT THE COURSE: 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.
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
Prof. Joydeep Dutta
