Computational Finance
Lecture 7- Stochastic Volatility Models
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This course is based on the book:
"Mathematical Modeling and Computation in Finance: With Exercises and Python and MATLAB Computer Codes", by C.W. Oosterlee and L.A. Grzelak, World Scientific Publishing, 2019.
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- Codes and the slides can be found at: https://github.com/LechGrzelak/Comput...
- See https://quantfinancebook.com/ for more details and for additional materials.
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0:00 Introduction
3:38 Towards Stochastic Volatility
16:55 The Stochastic Volatility Model of Heston
28:30 Correlated Stochastic Differential Equations
51:32 Ito’s Lemma for Vector Processes
1:01:04 Pricing PDE for the Heston Model
1:13:22 Impact of SV Model Parameters on Implied Volatility
1:22:41 Black-Scholes vs. Heston Model
1:30:17 Characteristic Function for the Heston Model
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CONTENT OF THIS COURSE:
Lecture 1- Introduction and Overview of Asset Classes
Lecture 2- Stock, Options and Stochastics
Lecture 3- Option Pricing and Simulation in Python
Lecture 4- Implied Volatility
Lecture 5- Jump Processes
Lecture 6- Affine Jump Diffusion Processes
***** Lecture 7- Stochastic Volatility Models
Lecture 8- Fourier Transformation for Option Pricing
Lecture 9- Monte Carlo Simulation
Lecture 10- Monte Carlo Simulation of the Heston Model
Lecture 11- Hedging and Monte Carlo Greeks
Lecture 12- Forward Start Options and Model of Bates
Lecture 13- Exotic Derivatives
Lecture 14- Summary

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