Columbia University - Computational Methods in Pricing and Model Calibration
- Offered byCoursera
Computational Methods in Pricing and Model Calibration at Coursera Overview
Duration | 24 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Intermediate |
Official Website | Explore Free Course  |
Credential | Certificate |
Computational Methods in Pricing and Model Calibration at Coursera Highlights
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Course 5 of 5 in the Financial Engineering and Risk Management Specialization
- Intermediate Level Students should have intermediate to advanced undergraduate courses in: (i) probability and statistics, (ii) linear algebra, and (iii) calculus.
- Approx. 24 hours to complete
- English Subtitles: English
Computational Methods in Pricing and Model Calibration at Coursera Course details
- This course focuses on computational methods in option and interest rate, products 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.
Computational Methods in Pricing and Model Calibration at Coursera Curriculum
Course Overview
Course Overview
About Us
Option Pricing and Numerical Approach
2.1a Introduction to Options: Calls, Puts, and a Speculator Example
2.1b Introduction to Options: a Hedger Example
2.2 Terms of Option Pricing and Pictorial Explanation
2.3a Option Pricing via Numerical Integration
2.3b The lognormal case
2.3c Python Code
2.4a Fourier Transform, Inverse Fourier Transform, and Characteristic Function
2.4b Call Price via the Inverse Fourier Transform
2.5 Numerical Evaluation of the Integral
2.6a Pricing Several Options Using FFT
2.6b Implementation of FFT
2.6c Python Code: Sanity Check for FFT
2.6d Python Code: Comparing Running Times with FFT
2.7a Case studies: Recap and Choice of Parameters
2.7b Case studies: BMS, Heston, and VG
2.7c Case studies: Findings and Observations
2.7d Case Studies: Python Code
Option Pricing Quiz
Option Pricing Assignment Part IV
Option Pricing Assignment (ungraded)
Model Calibration
3.1 Bid and Ask Prices and the Option Surface
3.2 Calibration and Implied Volatility
3.3 Objective Functions and the "Calibration Recipe"
3.4a Finding a Good Initial Parameter Set
3.4b Python Code
3.5a Optimization Routines: Brute-force Search
3.5b Python Code
3.6a Optimization Routines: the Nelder-Mead Algorithm
3.6b Python code
3.7a Optimization Routines: the BFGS Algorithm
3.7b Python Code
Model Calibration Quiz
Model Calibration Assignment
Interest Rates and Interest Rate Instruments Part I
4.1a Zero-Coupon Bond
4.1b Forward Contracts and Simple Forward Rate
4.1c Spot Rate and Instantaneous Spot Rate
4.1d Python Code
4.2a Swap Rates
4.2b Swap Rates Calculation
4.3a LIBOR Curves and Cross-Correlation
4.3b Swap Curves and Cross-Correlation
4.3c Python Code
4.4 Regression Using Least Squares
4.5a Regression using Nelder-Mead
4.5b Regression using Gradient Descent
4.5c Python Code
4.6 Vasicek Model and Calibration
4.7 CIR Model and Calibration
Interest Rate Instruments I
Interest Rate Instruments Assignment Part III
Interest Rates and Interest Rate Instruments Part II
5.1a Regression Using Least Squares
5.1b Python Code
5.2 Regression using Nelder-Mead
5.3 Regression using Gradient Descent
5.4 Vasicek Model and Calibration
5.5a CIR Model and Calibration
5.5b Python Code
Interest Rate Instruments II
Interest Rate Instruments Assignment Part IV
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Computational Methods in Pricing and Model Calibration