Computational Methods in Pricing and Model Calibration

Go to Course: https://www.coursera.org/learn/financial-engineering-computationalmethods

Introduction

### Course Review: Computational Methods in Pricing and Model Calibration on Coursera #### Overview The "Computational Methods in Pricing and Model Calibration" course offered on Coursera is a comprehensive program designed for those who want to deepen their understanding of computational techniques in the pricing of financial products, particularly options and interest rate instruments. Covering fundamental theories and practical applications, this course is ideal for finance professionals, quantitative analysts, and students looking to enhance their skillset in financial modeling. #### Course Structure and Content The course is divided into four substantive modules that build upon each other: 1. **Option Pricing and Numerical Approach**: This first module sets the stage by introducing various types of options available in the market. You'll delve into numerical techniques necessitated by the inability to derive analytic solutions for certain options. The focus here is on advanced models such as the Black-Merton-Scholes (BMS), Heston, and Variance Gamma (VG). The integration of Python coding throughout allows learners to apply theoretical knowledge practically, culminating in an assignment that challenges you to price different options under varying stock dynamics. 2. **Model Calibration**: Building on the previous week, this module addresses the critical task of model calibration—how to select models and set parameters. You'll gain insight into bid and ask prices, option surfaces, and guided calibration strategies. Different optimization algorithms (brute-force search, Nelder-Mead, and BFGS) are introduced, with hands-on Python coding to reinforce your understanding. An assignment focuses on practical application of model calibration techniques, ensuring that learners can convert theory into practice. 3. **Interest Rates and Interest Rate Instruments Part I**: The course transitions to interest rates, starting with fundamental concepts such as forward and spot rates, swap rates, and the term structures of interest rates. You'll learn how to calibrate the LIBOR and swap curves, tying together economic concepts with quantitative skills. Practical applications such as pricing bonds using collected data and implemented Python code offer a robust understanding of interest rate products. 4. **Interest Rates and Interest Rate Instruments Part II**: The final module applies regression analysis to model interest rate processes, focusing on techniques vital for market practitioners. You’ll explore the Vasicek and Cox-Ingersoll-Ross (CIR) models, and incorporate regression to fit market data effectively. Real-world applications ensure that learners gain relevant experience in managing illiquid interest rate products and deepening their understanding of fixed-income securities. #### Pros and Cons **Pros**: - **Applied Learning**: The emphasis on Python coding allows for hands-on experience, making the complex theories actionable. - **Expert Instruction**: The course is led by industry professionals who offer valuable insights into real-world applications of the techniques taught. - **Comprehensive Coverage**: Starting from options pricing to interest rate modeling, the course provides a well-rounded education that prepares students for various financial challenges. **Cons**: - **Requires Background Knowledge**: The course may be challenging for absolute beginners in quantitative finance or programming, as it builds upon prior knowledge of financial concepts. - **Time Commitment**: Given the depth of content, learners should be prepared to invest considerable time to fully engage with the material and complete assignments. #### Recommendation If you are aiming to enhance your capabilities in the field of finance, particularly in option pricing and model calibration, this course is highly recommended. The structured approach, practical applications, and expert guidance make it an invaluable resource for anyone looking to bolster their quantitative finance skills. Whether you are a professional looking to refine your expertise or a student eager to learn about advanced financial modeling, "Computational Methods in Pricing and Model Calibration" on Coursera is a course that will undoubtedly add considerable value to your educational journey. ### Conclusion Take the plunge into the world of computational finance and arm yourself with the knowledge that can set you apart in this highly competitive field. Consider enrolling in this course today and watch your understanding—and career prospects—soar.

Syllabus

Course Overview

In this week, we will study option pricing via a numerical approach. In many cases, analytical (explicit) solution of option prices is not obtainable, which requires numerical solutions. For example, if we switch the stock dynamics from geometric Brownian motion to another model, or switch the option from vanilla style to exotic style, explicit pricing formula will become unrealistic. Firstly, we start from introduction to options, where you can learn different types of options and different perspectives of option market participants. Then we will talk about option pricing via numerical integration both in general and in details. In particular, we will focus on Fourier transform and fast Fourier transform (FFT). We also provide Python codes for you to learn how to apply these techniques in practice. In the end of this week, you will be exposed to several cases studies, from time cost comparison to different models. There are lots of models which estimates the stock price evolution. Among these models, we will mainly focus on Black-Merton-Scholes (BMS), Heston, and Variance Gamma (VG) model, where you will learn the motivation and characteristic of each model. Afterwards, you will have an assignment about option pricing, where you can utilize all the theoretical knowledge and Python codes to price different options under different stock dynamics.

In this week, we will study model calibration, which follows the topics in last week. You have been exposed to many models, but you have no information about how to choose the model and parameters. Fortunately, you will learn how to solve this problem in this week from different approaches. Firstly, we start from an introduction to bid and ask prices and option surface. Then we will talk about the model calibration in regards with fitting the market option price, also with pictorial demonstration about implied volatility. Next, you will learn the calibration recipe, involving objective functions and initial parameter set. You will also learn how to do calibration in practice, which is an optimization problem. We will introduce three routines: brute-force search, Nelder-Mead algorithm, and BFGS algorithm. Except from learning these routines theoretically, you will also learn how to apply them in the optimization problem from Python codes. Followingly, you can apply what you learn about calibration in the assignment.

We will start learning interest rates and interest rate instruments from this week. Interest rates play a very important role in measuring the future and present value of financial products. People also use market interest rates to analyze the economic situation. At the very beginning, we will introduce fundamental interest rate concepts, including forward rates, spot rates, swap rates and term structures of interest rates. Then we will apply data-driven analysis to calibrate LIBOR and swap curves and cross-correlations between these rates. Using the term structure of these interest rates, we should be able to price market value of bonds, swaps and other interest rate products. We also provide you with Python codes in order to show how to obtain the LIBOR curve and how to use it to price bonds. After learning this module, you will have a brief overview of interest rates and their applications in bond and swap pricing. We will talk about complex stochastic models and calibrate interest curves with these models next week.

This week we will use different models to estimate interest rate processes and implement regression analysis to calibrate the processes. The models in this week are very important in practice. For instance, market makers need good models to help them interpolate or extrapolate market prices of illiquid interest-rate products, while speculators need models to help them understand the prices of fixed income securities so that they can bet on interest rates, etc. So in this module, we will first provide different regression techniques used to fit data in the market. Then we will introduce Vasicek model and CIR model for bond pricing. We also show how to use regression to fit data with our models. We provide all codes needed and also go through the codes to help you know how to apply them. At the end of the lecture, you will be asked to practice interest rate models by fitting LIBOR rates in the assignment.