## 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

- Advanced Matrix Theory and Linear Algebra for Engineers by IISc Bangalore
- Mathematics II by IIT Roorkee
- Differential Equations II by Khan Academy
- Discrete Mathematics I by IIT Roorkee
- Linear programming and Extensions by IIT Kanpur
- Discrete Structures by IIT Madras
- Algebra 2 by Other
- Pre-algebra by Khan Academy
- Stochastic Processes by IIT Delhi
- A Basic Course in Real Analysis by IIT Kharagpur

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