## Course Description :

Contents:

Binomial Model; No Arbitrage; Numeraires; Replication - Multi-period binomial model; CRR trees; continuous time limit; default model-Measure change and sample paths; Price Sensitivity; incomplete markets, variance minimizing hedge - Interest Rate Models; IR Calibration; Arrow - Debreu; Discrete Forward Fokker - Planck Equations-IR Trees, continuous time limit, Vasicek model, simultaion, CCIRS

Stochastic Calculus overview - Continuous Time Dynamic Hedging-Solutions of the Black - Scholes PDE; Feynman-Kac; Time-based/Move-based hedging, Delta-Gamma-Vega hedging - More on Feynman-Kac, Measure Changes, Continuous Time Interest Rate Models -Measure Changes and Numeraires, Bond Options-More on numeraire measures, interest rate tree - Foreign Exchange - Credit Derivatives-Commodity Modeling - Regime Switching and Jump Models - More on jump models-Tutorial review and Heston Model - LFM and LSM - more on LFM and LSM

## Other Resources :

## Other Mathematics Courses

- Linear Algebra - Khan Academy by Khan Academy
- Linear Algebra by MIT
- Probability and Random Processes by IIT Kharagpur
- Probability by Khan Academy
- Measure and Integration by IIT Bombay
- An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by IIT Madras
- Formal Languages and Automata Theory by IIT Guwahati
- Algebra 2 by Other
- Engineering Mathematics by The University of New South Wales
- Pre Algebra by Other

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