Probability and Stochastics for Finance

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