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.
Monthly Subscription Starting at AED 99 + VAT
- Level Professional
- Duration 24 hours
- Course by Columbia University
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Offered by
About
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.Modules
Course Overview
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3
Readings
3
Readings
- Course Overview
- About Us
- Academic Honesty Policy
Option Pricing
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17
Videos
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2
Readings
17
Videos
- 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
2
Readings
- Lesson Supplement
- Python Code Files
Review
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1
Assignment
1
Assignment
- Option Pricing Quiz
Assignment
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1
Readings
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1
Lab
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2
Assignment
2
Assignment
- Option Pricing Assignment Part IV
- Option Pricing Assignment (ungraded)
1
Labs
- Option Pricing Python Notebook
1
Readings
- Option Pricing Assignment Part IV Solution
Lectures
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11
Videos
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2
Readings
11
Videos
- 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
2
Readings
- Lesson Supplement
- Python Code Files
Review
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1
Assignment
1
Assignment
- Model Calibration Quiz
Assignment
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1
Lab
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1
Assignment
1
Assignment
- Model Calibration Assignment
1
Labs
- Model Calibration Assignment
Interest Rate Instruments Part I
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9
Videos
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2
Readings
9
Videos
- 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
2
Readings
- Lesson Supplement
- Python Code Files
Review
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1
Assignment
1
Assignment
- Interest Rate Instruments I
Assignment
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1
Lab
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1
Assignment
1
Assignment
- Interest Rate Instruments Assignment Part III
1
Labs
- Interest Rate Instruments Notebook 1
Interest Rate Instruments Part II
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8
Videos
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2
Readings
8
Videos
- 5.1a Regression Using Least Squares
- 5.1b Python Code
- 5.2 Regression using Nelder-Mead
- 5.3 Regression using Gradient Descent
- 5.3b Python Code
- 5.4 Vasicek Model and Calibration
- 5.5a CIR Model and Calibration
- 5.5b Python Code
2
Readings
- Lesson Supplement
- Python Code Files
Review
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1
Assignment
1
Assignment
- Interest Rate Instruments II
Assignment
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1
Lab
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1
Assignment
1
Assignment
- Interest Rate Instruments Assignment Part IV
1
Labs
- Interest Rate Instruments Notebook 2
Auto Summary
"Computational Methods in Pricing and Model Calibration" is a professional course offered by Coursera, focusing on advanced computational techniques for pricing options and interest rate products, and model calibration. Led by expert instructors, it covers key models like Black-Merton-Scholes, Heston, and Variance Gamma, and delves into bid-ask prices, implied volatility, and option surfaces. Learners will engage with practical Python coding examples and optimization routines. Ideal for professionals in business and management, the course spans 1440 minutes and offers a starter subscription option.
Garud Iyengar
Ali Hirsa
Martin Haugh