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Columbia University

Computational Methods in Pricing and Model Calibration

This course focuses on computational methods in option and interest rate, product’s pricing and model calibration. The first module will introduce different types of options in the market, followed by an in-depth discussion into numerical techniques helpful in pricing them, e.g. Fourier Transform (FT) and Fast Fourier Transform (FFT) methods. We will explain models like Black-Merton-Scholes (BMS), Heston, Variance Gamma (VG), which are central to understanding stock price evolution, through case studies and Python codes. The second module introduces concepts like bid-ask prices, implied volatility, and option surfaces, followed by a demonstration of model calibration for fitting market option prices using optimization routines like brute-force search, Nelder-Mead algorithm, and BFGS algorithm. The third module introduces interest rates and the financial products built around these instruments. We will bring in fundamental concepts like forward rates, spot rates, swap rates, and the term structure of interest rates, extending it further for creating, calibrating, and analyzing LIBOR and swap curves. We will also demonstrate the pricing of bonds, swaps, and other interest rate products through Python codes. The final module focuses on real-world model calibration techniques used by practitioners to estimate interest rate processes and derive prices of different financial products. We will illustrate several regression techniques used for interest rate model calibration and end the module by covering the Vasicek and CIR model for pricing fixed income instruments.

状态:Case Studies
状态:Applied Mathematics
中级课程小时

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JT

5.0评论日期:Jun 24, 2025

Good level of mathematical content and coding. At first I wasn't a fan of the excel components but they do force you to learn the methods in a different way and could be the tool used in industry.

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skanuri
5.0
评论日期:Jun 1, 2023
Alina Caraiman
5.0
评论日期:Apr 7, 2025
Jack Templeton
5.0
评论日期:Jun 25, 2025
daniel hurtado
5.0
评论日期:Oct 5, 2022
Hao Hu
5.0
评论日期:Jul 3, 2024
Marco Pulido
5.0
评论日期:Feb 7, 2025
Sheng Zhang
5.0
评论日期:Jul 28, 2024
Sandra JR
5.0
评论日期:Nov 7, 2024
Kostya Titorenko
4.0
评论日期:Sep 19, 2021
Murray Sondergard
4.0
评论日期:Oct 19, 2021
Angela Torres
3.0
评论日期:Feb 26, 2023
J
1.0
评论日期:Feb 3, 2022