## 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

- Stochastic Processes by IIT Delhi
- Complex Analysis by IIT Guwahati
- California Standards Test: Geometry by Khan Academy
- Introduction to Probability and Statistics,Fall 2011 by UC Berkeley
- University Algebra by The University of New South Wales
- Formal Languages and Automata Theory by IIT Guwahati
- Differential Equations by MIT
- Linear programming and Extensions by IIT Kanpur
- Statistics by Khan Academy
- Introduction to Geometry by Other

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